{"id":5687,"date":"2026-06-30T20:20:30","date_gmt":"2026-06-30T14:50:30","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=5687"},"modified":"2026-06-30T20:20:41","modified_gmt":"2026-06-30T14:50:41","slug":"ncert-class-10-maths-exercise-4-2-solutions-factorisation-method","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-exercise-4-2-solutions-factorisation-method\/","title":{"rendered":"NCERT Class 10 Maths Exercise 4.2 Solutions | Factorisation Method"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-248386297\"><div id=\"mymoc-362691039\"><a href=\"https:\/\/amzn.to\/4upqwUD\" aria-label=\"laptop-1\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1.png 1303w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-300x91.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-1024x310.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/laptop-1-768x233.png 768w\" sizes=\"(max-width: 1303px) 100vw, 1303px\" width=\"1303\" height=\"395\"><\/a><\/div><\/div><div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5687?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">9<\/span><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Short Introduction<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 4.2 introduces one of the easiest and most powerful methods of solving quadratic equations&mdash;the <strong>Factorisation Method<\/strong>. In this exercise, students learn how to split the middle term, factorise quadratic expressions, and apply the Zero Product Property to obtain the roots of quadratic equations. The exercise also includes real-life word problems involving ages, distances, geometry, and production costs.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Quick Information Box<\/h1>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Particular<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Class<\/td><td>10<\/td><\/tr><tr><td>Subject<\/td><td>Mathematics<\/td><\/tr><tr><td>Chapter<\/td><td>4<\/td><\/tr><tr><td>Chapter Name<\/td><td>Quadratic Equations<\/td><\/tr><tr><td>Exercise<\/td><td>4.2<\/td><\/tr><tr><td>Board<\/td><td>CBSE<\/td><\/tr><tr><td>Method Used<\/td><td>Factorisation<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Moderate<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Learning Objectives<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">After completing this exercise, students will be able to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solve quadratic equations using factorisation.<\/li>\n\n\n\n<li>Apply Zero Product Property.<\/li>\n\n\n\n<li>Verify obtained roots.<\/li>\n\n\n\n<li>Solve application-based word problems.<\/li>\n\n\n\n<li>Improve algebraic manipulation skills.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Quadratic Equations<\/li>\n\n\n\n<li>Standard Form<\/li>\n\n\n\n<li>Factorisation<\/li>\n\n\n\n<li>Splitting Middle Term<\/li>\n\n\n\n<li>Zero Product Property<\/li>\n\n\n\n<li>Verification of Roots<\/li>\n\n\n\n<li>Word Problems<\/li>\n\n\n\n<li>Algebraic Expressions<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Important Formulas<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Standard Form<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>=<\/mo><mn>0<\/mn><mo separator=\"true\">,<\/mo><mspace width=\"2em\"><\/mspace><mi>a<\/mi><mo mathvariant=\"normal\">&ne;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ax^2+bx+c=0,\\qquad a\\neq0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Zero Product Property<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">If<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">AB=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">or<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Sum of Consecutive Numbers<\/h2>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-real-number-exercise-1-2-solutions-mymockmate\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 10 Maths Real Number Exercise 1.2 Solutions |  MyMockMate<\/span><\/a><\/div><p class=\"wp-block-paragraph\">If first number is<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then second number is<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x+1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Area of Rectangle<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>r<\/mi><mi>e<\/mi><mi>a<\/mi><mo>=<\/mo><mi>L<\/mi><mi>e<\/mi><mi>n<\/mi><mi>g<\/mi><mi>t<\/mi><mi>h<\/mi><mo>&times;<\/mo><mi>B<\/mi><mi>r<\/mi><mi>e<\/mi><mi>a<\/mi><mi>d<\/mi><mi>t<\/mi><mi>h<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Area=Length\\times Breadth<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Distance Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>D<\/mi><mi>i<\/mi><mi>s<\/mi><mi>t<\/mi><mi>a<\/mi><mi>n<\/mi><mi>c<\/mi><mi>e<\/mi><mo>=<\/mo><mi>S<\/mi><mi>p<\/mi><mi>e<\/mi><mi>e<\/mi><mi>d<\/mi><mo>&times;<\/mo><mi>T<\/mi><mi>i<\/mi><mi>m<\/mi><mi>e<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">Distance=Speed\\times Time<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exercise 4.2<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Question 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Find the roots of the following quadratic equations by factorisation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1(i)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mn>3<\/mn><mi>x<\/mi><mo>&minus;<\/mo><mn>10<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2-3x-10=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img fetchpriority=\"high\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-270-819x1024.png\" alt=\"\" class=\"wp-image-5815\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-270-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-270-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-270-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-270.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1(ii)<\/h1>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-1-solutions-polynomials-ncert-solutions\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">NCERT Class 10 Maths Exercise 2.1 Solutions | Polynomials<\/span><\/a><\/div><p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>6<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x^2+x-6=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-271-819x1024.png\" alt=\"\" class=\"wp-image-5817\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-271-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-271-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-271-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-271.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1(iii)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msqrt><mn>2<\/mn><\/msqrt><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>7<\/mn><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><msqrt><mn>2<\/mn><\/msqrt><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\sqrt2x^2+7x+5\\sqrt2=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"930\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-273-930x1024.png\" alt=\"\" class=\"wp-image-5820\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-273-930x1024.png 930w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-273-272x300.png 272w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-273-768x846.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-273.png 1195w\" sizes=\"(max-width: 930px) 100vw, 930px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1(iv)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mi>x<\/mi><mo>+<\/mo><mfrac><mn>1<\/mn><mn>8<\/mn><\/mfrac><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x^2-x+\\frac18=0<\/annotation><\/semantics><\/math><\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-2792411877\"><div id=\"mymoc-3020402812\"><a href=\"https:\/\/amzn.to\/4xnw9oY\" aria-label=\"head-phones\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-300x80.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-1024x274.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/head-phones-768x205.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1301\" height=\"348\"><\/a><\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"819\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-274-819x1024.png\" alt=\"\" class=\"wp-image-5825\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-274-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-274-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-274-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-274.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1(v)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mn>100<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mn>20<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">100x^2-20x+1=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"683\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272-683x1024.png\" alt=\"\" class=\"wp-image-5818\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-272.png 1024w\" sizes=\"(max-width: 683px) 100vw, 683px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Solve the problems given in Example 1.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Example 1 has two problems:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>John and Jivanti together have 45 marbles. Both lost 5 marbles each. The product of the marbles left with them is 124.<\/li>\n\n\n\n<li>A cottage industry produces toys. The cost of each toy is &#8377;55 minus the number of toys produced. Total production cost is &#8377;750.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2(i)<\/h1>\n\n\n\n<div class=\"internal-linking-related-contents\"><a href=\"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-2-solutions-relationship-between-zeroes-and-coefficients\/\" class=\"template-2\"><span class=\"cta\">Related Topic to Read more<\/span><span class=\"postTitle\">Class 10 Maths Exercise 2.2 Solutions | Relationship Between Zeroes and Coefficients<\/span><\/a><\/div><p class=\"wp-block-paragraph\">John and Jivanti together have 45 marbles. Both lost 5 marbles each, and the product of the number of marbles they now have is 124. Find how many marbles they had to start with.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-279-859x1024.png\" alt=\"\" class=\"wp-image-5840\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-279-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-279-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-279-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-279.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 2(ii)<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A cottage industry produces a certain number of toys in a day. The cost of production of each toy was found to be &#8377;55 minus the number of toys produced in a day. On a particular day, the total cost of production was &#8377;750. Find the number of toys produced on that day.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\"><\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"859\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-280-1024x859.png\" alt=\"\" class=\"wp-image-5842\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-280-1024x859.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-280-300x252.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-280-768x645.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-280.png 1369w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 3<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find two numbers whose sum is 27 and product is 182.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"890\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-275-890x1024.png\" alt=\"\" class=\"wp-image-5829\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-275-890x1024.png 890w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-275-261x300.png 261w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-275-768x884.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-275.png 1169w\" sizes=\"(max-width: 890px) 100vw, 890px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 4<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Find two consecutive positive integers, sum of whose squares is 365.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-276-859x1024.png\" alt=\"\" class=\"wp-image-5831\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-276-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-276-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-276-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-276.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 5<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>The altitude of a right triangle is 7 cm less than its base. If the hypotenuse is 13 cm, find the other two sides.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Solution<\/h2>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"837\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-277-837x1024.png\" alt=\"\" class=\"wp-image-5835\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-277-837x1024.png 837w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-277-245x300.png 245w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-277-768x939.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-277.png 1134w\" sizes=\"(max-width: 837px) 100vw, 837px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Question 6<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">A cottage industry produces a certain number of pottery articles in a day. It was observed on a particular day that the cost of production of each article (in rupees) was <strong>&#8377;3 more than twice the number of articles produced<\/strong> on that day. If the <strong>total cost of production<\/strong> on that day was <strong>&#8377;90<\/strong>, find:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The number of articles produced.<\/li>\n\n\n\n<li>The cost of each article.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Solution<\/h1>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-278-859x1024.png\" alt=\"\" class=\"wp-image-5837\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-278-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-278-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-278-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-278.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exercise 4.2 Summary<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">After completing Exercise 4.2, students should be able to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Solve quadratic equations using factorisation.<\/li>\n\n\n\n<li>Split the middle term correctly.<\/li>\n\n\n\n<li>Apply the Zero Product Property.<\/li>\n\n\n\n<li>Verify the obtained roots.<\/li>\n\n\n\n<li>Solve real-life application problems based on quadratic equations.<\/li>\n\n\n\n<li>Choose only meaningful (positive) solutions in practical problems.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Many students lose marks due to small calculation errors. Avoid these common mistakes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Incorrect Middle-Term Splitting<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Choose numbers whose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Product = <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mo>&times;<\/mo><mi>c<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">a \\times c<\/annotation><\/semantics><\/math>a&times;c<\/li>\n\n\n\n<li>Sum = coefficient of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><\/mrow><annotation encoding=\"application\/x-tex\">x<\/annotation><\/semantics><\/math>x<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">2. Forgetting Standard Form<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Always write the equation as<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>a<\/mi><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mi>b<\/mi><mi>x<\/mi><mo>+<\/mo><mi>c<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ax^2+bx+c=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">before factorising.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">3. Sign Errors<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Most mistakes occur while transferring terms from one side of the equation to the other.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Always recheck the signs.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">4. Wrong Common Factor<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">While grouping terms, ensure both groups have the same common binomial.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">5. Ignoring Verification<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Always substitute the obtained roots into the original equation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">6. Accepting Negative Measurements<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">In word problems involving:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Age<\/li>\n\n\n\n<li>Distance<\/li>\n\n\n\n<li>Length<\/li>\n\n\n\n<li>Breadth<\/li>\n\n\n\n<li>Number of objects<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Reject negative answers because they have no practical meaning.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Exam Tips<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">&#10004; Learn tables up to 30.<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Factorisation becomes much faster.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">&#10004; Memorise perfect squares<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Examples<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>+<\/mo><mi>b<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(a+b)^2<\/annotation><\/semantics><\/math><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>a<\/mi><mo>&minus;<\/mo><mi>b<\/mi><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">(a-b)^2<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">These frequently appear in quadratic equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">&#10004; Write every algebraic step<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">CBSE awards step-wise marks.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">&#10004; Verify every answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Substitute each root into the original equation.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">&#10004; Practice daily<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Quadratic equations improve only through regular practice.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Practice MCQs<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Question 1<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Which method is used in Exercise 4.2?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Graph Method<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Elimination Method<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Factorisation Method<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Matrix Method<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 2<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The Zero Product Property states that if<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">AB=0<\/annotation><\/semantics><\/math>AB=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. A=0 only<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. B=0 only<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Either A=0 or B=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. None<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 3<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The roots of<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(x-5)(x+2)=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">are<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 5,2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. -5,-2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 5,-2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 2,-5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 4<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The equation<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mi>x<\/mi><mo>&minus;<\/mo><mn>1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">(4x-1)^2=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">has<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. One repeated root<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Two distinct roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. No real roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Three roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> A<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 5<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Which property is used after factorisation?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Midpoint Theorem<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Pythagoras Theorem<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Zero Product Property<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Euclid Division Lemma<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> C<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 6<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The quadratic equation<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mn>27<\/mn><mi>x<\/mi><mo>+<\/mo><mn>182<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2-27x+182=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">has roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 12 and 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 13 and 14<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 10 and 17<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 11 and 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 7<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">A quadratic equation has maximum<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. 1 root<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 2 roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 3 roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 4 roots<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 8<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Which chapter introduces solving quadratic equations by factorisation?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Pair of Linear Equations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Quadratic Equations<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Triangles<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Probability<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 9<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Before factorisation, every quadratic equation should be written in:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Expanded Form<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Standard Form<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Simplified Form<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Graphical Form<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Question 10<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The roots obtained should always be:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A. Memorised<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. Verified<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. Rounded<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. Ignored<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#9989; <strong>Answer:<\/strong> B<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Frequently Asked Questions (FAQ)<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Q1. What is the factorisation method?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">It is a method of solving quadratic equations by expressing the quadratic polynomial as the product of two linear factors and then applying the Zero Product Property.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q2. What is the Zero Product Property?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">If<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mi>B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">AB=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">then<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>A<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">A=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">or<math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mi>B<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">B=0<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q3. Why do we verify roots?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Verification ensures that the obtained values satisfy the original equation and helps avoid calculation mistakes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q4. Can a quadratic equation have equal roots?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. If both factors are identical, the equation has two equal (repeated) roots.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q5. Why are negative answers rejected in some word problems?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Quantities such as age, length, speed, distance, and the number of objects cannot be negative in real-life situations, so only meaningful positive solutions are accepted.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q6. Which method is used in Exercise 4.2?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 4.2 focuses on solving quadratic equations using the <strong>factorisation method<\/strong> before introducing the quadratic formula in later sections.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Final Revision Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>&#10004; Convert every equation into standard form.<\/li>\n\n\n\n<li>&#10004; Split the middle term carefully.<\/li>\n\n\n\n<li>&#10004; Factorise correctly.<\/li>\n\n\n\n<li>&#10004; Apply the Zero Product Property.<\/li>\n\n\n\n<li>&#10004; Verify both roots.<\/li>\n\n\n\n<li>&#10004; Reject invalid negative values in application-based questions.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"wp-block-paragraph\">&#127919; <strong>Practice More, Score More with MyMockMate!<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Master <strong>NCERT Class 10 Maths Chapter 4 &ndash; Quadratic Equations<\/strong> through detailed chapter-wise solutions, concept notes, MCQs, assertion&ndash;reason questions, previous year questions, mock tests, and exam-oriented study material.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&#128216; Visit <strong><a href=\"http:\/\/www.mymockmate.com\">www.mymockmate.com<\/a><\/strong> for:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Complete NCERT Solutions<\/li>\n\n\n\n<li>Chapter-wise Notes<\/li>\n\n\n\n<li>CBSE Mock Tests<\/li>\n\n\n\n<li>Important Questions<\/li>\n\n\n\n<li>Practice Worksheets<\/li>\n\n\n\n<li>Previous Year Papers<\/li>\n\n\n\n<li>Exam Preparation Resources<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Keep practicing consistently, verify every solution, and you&rsquo;ll build strong confidence in solving quadratic equations for your CBSE exams.<\/strong><\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5687?print=print\" class=\"pdfprnt-button pdfprnt-button-print\" target=\"_blank\"><img decoding=\"async\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/plugins\/pdf-print\/images\/print.png\" alt=\"image_print\" title=\"Print Content\"><span class=\"pdfprnt-button-title pdfprnt-button-print-title\">Print<\/span><\/a> <span class=\"pdfprnt-count-generation\">9<\/span><\/div><div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-2818865041\"><div id=\"mymoc-486689991\"><a href=\"https:\/\/amzn.to\/4ehJfM4\" aria-label=\"students acessories\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories.png 1301w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-300x85.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-1024x290.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/students-acessories-768x218.png 768w\" sizes=\"(max-width: 1301px) 100vw, 1301px\" width=\"1080\" height=\"100\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 9 Short Introduction Exercise 4.2 introduces one of the easiest and most powerful methods of solving quadratic equations&mdash;the Factorisation Method. In this exercise, students&#8230;<\/p>\n","protected":false},"author":1,"featured_media":5697,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[5,10],"tags":[3603,3602,70,96,3601,3605,3604],"class_list":["post-5687","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10","category-maths-class-10","tag-cbse-class-10-maths-solutions","tag-chapter-4-quadratic-equations","tag-class-10-maths-solutions","tag-factorisation-method","tag-ncert-class-10-maths-exercise-4-2-solutions","tag-ncert-maths-chapter-4-answers","tag-quadratic-equations-exercise-4-2"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/NCERT-Class-10-Maths-Exercise-4.2-Solutions.png","author_info":{"display_name":"Team Mymockmate","author_link":"https:\/\/mymockmate.com\/notes\/author\/bsm_adm\/"},"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5687","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/comments?post=5687"}],"version-history":[{"count":24,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5687\/revisions"}],"predecessor-version":[{"id":5845,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5687\/revisions\/5845"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/5697"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=5687"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=5687"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=5687"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}