{"id":5686,"date":"2026-06-29T20:51:06","date_gmt":"2026-06-29T15:21:06","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=5686"},"modified":"2026-06-30T18:23:35","modified_gmt":"2026-06-30T12:53:35","slug":"ncert-class-10-maths-exercise-4-1-solutions-quadratic-equations","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/ncert-class-10-maths-exercise-4-1-solutions-quadratic-equations\/","title":{"rendered":"NCERT Class 10 Maths Exercise 4.1 Solutions | Quadratic Equations"},"content":{"rendered":"<div class=\"mymoc-top mymoc-entity-placement\" id=\"mymoc-1007311998\"><div id=\"mymoc-2710358100\"><a href=\"https:\/\/amzn.to\/4fDWGbw\" aria-label=\"smartwatch\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png 1717w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-300x71.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1024x243.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-768x182.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1536x364.png 1536w\" sizes=\"(max-width: 1717px) 100vw, 1717px\" width=\"1717\" height=\"407\"><\/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\/5686?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\">11<\/span><\/div>\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">Short Introduction<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 4.1 introduces students to <strong>Quadratic Equations<\/strong>, one of the most important topics in Class 10 Mathematics. In this exercise, students learn how to:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Identify whether an equation is quadratic.<\/li>\n\n\n\n<li>Convert equations into standard form.<\/li>\n\n\n\n<li>Represent practical situations mathematically using quadratic equations.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">This exercise develops algebraic thinking and prepares students for solving quadratic equations in the next exercises.<\/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>Chapter<\/td><td>4<\/td><\/tr><tr><td>Chapter Name<\/td><td>Quadratic Equations<\/td><\/tr><tr><td>Exercise<\/td><td>4.1<\/td><\/tr><tr><td>Board<\/td><td>CBSE<\/td><\/tr><tr><td>Class<\/td><td>10<\/td><\/tr><tr><td>Topic<\/td><td>Identifying Quadratic Equations &amp; Forming Equations<\/td><\/tr><tr><td>Difficulty Level<\/td><td>Easy to 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\">Concepts Used (Topics Covered)<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Definition of Quadratic Equation<\/li>\n\n\n\n<li>Standard Form of Quadratic Equation<\/li>\n\n\n\n<li>Degree of Polynomial<\/li>\n\n\n\n<li>Expanding Algebraic Expressions<\/li>\n\n\n\n<li>Simplifying Equations<\/li>\n\n\n\n<li>Word Problems<\/li>\n\n\n\n<li>Mathematical Modelling<\/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<h3 class=\"wp-block-heading\">Standard Form<\/h3>\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<h3 class=\"wp-block-heading\">Degree of Quadratic Equation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Highest power of variable = <strong>2<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Area of Rectangle<\/h3>\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<h3 class=\"wp-block-heading\">Distance Formula<\/h3>\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<h3 class=\"wp-block-heading\">Consecutive Numbers<\/h3>\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<h1 class=\"wp-block-heading\">Exercise 4.1 Solutions<\/h1>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Check whether the following are quadratic equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(i)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><mo>=<\/mo><mn>2<\/mn><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(x+1)^2=2(x-3)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\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-258-819x1024.png\" alt=\"\" class=\"wp-image-5699\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-258-819x1024.png 819w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-258-240x300.png 240w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-258-768x960.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-258.png 1122w\" sizes=\"(max-width: 819px) 100vw, 819px\"><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\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>2<\/mn><mi>x<\/mi><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mo>&minus;<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>3<\/mn><mo>&minus;<\/mo><mi>x<\/mi><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">x^2-2x=(-2)(3-x)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"859\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-259-859x1024.png\" alt=\"\" class=\"wp-image-5701\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-259-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-259-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-259-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-259.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<h2 class=\"wp-block-heading\">(iii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>2<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(x-2)(x+1)=(x-1)(x+3)<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" width=\"862\" height=\"1024\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-260-862x1024.png\" alt=\"\" class=\"wp-image-5704\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-260-862x1024.png 862w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-260-253x300.png 253w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-260-768x912.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-260.png 1151w\" sizes=\"(max-width: 862px) 100vw, 862px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iv)<\/h2>\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><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mi>x<\/mi><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(x-3)(2x+1)=x(x+5)<\/annotation><\/semantics><\/math><\/p>\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-262-859x1024.png\" alt=\"\" class=\"wp-image-5708\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-262-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-262-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-262-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-262.png 1149w\" sizes=\"(max-width: 859px) 100vw, 859px\"><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\">(v)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mn>2<\/mn><mi>x<\/mi><mo>&minus;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>3<\/mn><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>5<\/mn><mo stretchy=\"false\">)<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(2x-1)(x-3)=(x+5)(x-1)<\/annotation><\/semantics><\/math><\/p>\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-261-683x1024.png\" alt=\"\" class=\"wp-image-5707\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-261-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-261-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-261-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-261-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-261.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<h2 class=\"wp-block-heading\">(vi)<\/h2>\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>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x^2+3x+1=(x-2)^2<\/annotation><\/semantics><\/math><\/p><div class=\"mymoc-middle mymoc-entity-placement\" id=\"mymoc-644741899\"><div id=\"mymoc-2085028856\"><a href=\"https:\/\/amzn.to\/4v5gV6P\" aria-label=\"calculators\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators.png 1302w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-300x99.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-1024x338.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/calculators-768x254.png 768w\" sizes=\"(max-width: 1302px) 100vw, 1302px\" width=\"1302\" height=\"430\"><\/a><\/div><\/div>\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-263-859x1024.png\" alt=\"\" class=\"wp-image-5710\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-263-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-263-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-263-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-263.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<h2 class=\"wp-block-heading\">(vii)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" display=\"block\"><semantics><mrow><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><mo>=<\/mo><mn>2<\/mn><mi>x<\/mi><mo stretchy=\"false\">(<\/mo><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mn>1<\/mn><mo stretchy=\"false\">)<\/mo><\/mrow><annotation encoding=\"application\/x-tex\">(x+2)^3=2x(x^2-1)<\/annotation><\/semantics><\/math><\/p>\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-264-683x1024.png\" alt=\"\" class=\"wp-image-5711\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-264-683x1024.png 683w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-264-200x300.png 200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-264-768x1152.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-264-600x900.png 600w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-264.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<h2 class=\"wp-block-heading\">(viii)<\/h2>\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>3<\/mn><\/msup><mo>&minus;<\/mo><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mi>x<\/mi><mo>+<\/mo><mn>1<\/mn><mo>=<\/mo><mo stretchy=\"false\">(<\/mo><mi>x<\/mi><mo>&minus;<\/mo><mn>2<\/mn><msup><mo stretchy=\"false\">)<\/mo><mn>3<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x^3-4x^2-x+1=(x-2)^3<\/annotation><\/semantics><\/math><\/p>\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-265-859x1024.png\" alt=\"\" class=\"wp-image-5713\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-265-859x1024.png 859w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-265-252x300.png 252w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-265-768x915.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-265.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<\/h1>\n\n\n\n<p class=\"wp-block-paragraph\">Represent the following situations in the form of quadratic equations.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(i) The area of a rectangular plot is 528 m<sup>2<\/sup>. The length of the plot (in metres) is one more than twice its breadth. We need to find the length and breadth of the plot.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-266-1024x819.png\" alt=\"\" class=\"wp-image-5715\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-266-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-266-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-266-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-266.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(ii) The product of two consecutive positive integers is 306. We need to find the integers.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-267-1024x819.png\" alt=\"\" class=\"wp-image-5719\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-267-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-267-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-267-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-267.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iii) Rohan&rsquo;s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan&rsquo;s present age.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"819\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-268-1024x819.png\" alt=\"\" class=\"wp-image-5723\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-268-1024x819.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-268-300x240.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-268-768x615.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-268.png 1402w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h2 class=\"wp-block-heading\">(iv) (iv) A train travels a distance of 480 km at a uniform speed. If the speed had been 8 km\/h less, then it would have taken 3 hours more to cover the same distance. We need to find the speed of the train.<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"683\" src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269-1024x683.png\" alt=\"\" class=\"wp-image-5726\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269-1024x683.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269-300x200.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269-768x512.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269-1200x800.png 1200w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/image-269.png 1536w\" sizes=\"(max-width: 1024px) 100vw, 1024px\"><\/figure>\n\n\n\n<h1 class=\"wp-block-heading\">Common Mistakes<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Forgetting to convert the equation into standard form.<\/li>\n\n\n\n<li>Not expanding brackets correctly.<\/li>\n\n\n\n<li>Assuming every equation containing <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x^2<\/annotation><\/semantics><\/math>x2 is quadratic without simplification.<\/li>\n\n\n\n<li>Missing sign changes while shifting terms.<\/li>\n\n\n\n<li>Writing incorrect expressions in word 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\">Exam Tips<\/h1>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always simplify the equation first.<\/li>\n\n\n\n<li>Check the highest power after simplification.<\/li>\n\n\n\n<li>Ensure the coefficient of <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><\/mrow><annotation encoding=\"application\/x-tex\">x^2<\/annotation><\/semantics><\/math>x2 is not zero.<\/li>\n\n\n\n<li>For word problems, define the variable clearly before forming the equation.<\/li>\n\n\n\n<li>Write the final quadratic equation in standard form.<\/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\">Practice MCQs<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">1. A quadratic equation has degree<\/h3>\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\">A. 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 4<\/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<h3 class=\"wp-block-heading\">2. Which is the standard form?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>a<\/mi><mi>x<\/mi><mo>+<\/mo><mi>b<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ax+b=0<\/annotation><\/semantics><\/math>ax+b=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><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>ax2+bx+c=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^3+x=0<\/annotation><\/semantics><\/math>x3+x=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mi>x<\/mi><mo>+<\/mo><mn>2<\/mn><mo>=<\/mo><mn>3<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x+2=3<\/annotation><\/semantics><\/math>x+2=3<\/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<h3 class=\"wp-block-heading\">3. Which is NOT a quadratic equation?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>5<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^2+5=0<\/annotation><\/semantics><\/math>x2+5=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>2<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>+<\/mo><mn>3<\/mn><mi>x<\/mi><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">2x^2+3x=1<\/annotation><\/semantics><\/math>2&times;2+3x=1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><msup><mi>x<\/mi><mn>3<\/mn><\/msup><mo>+<\/mo><mi>x<\/mi><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">x^3+x=0<\/annotation><\/semantics><\/math>x3+x=0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. <math xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mn>4<\/mn><msup><mi>x<\/mi><mn>2<\/mn><\/msup><mo>&minus;<\/mo><mn>9<\/mn><mo>=<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">4x^2-9=0<\/annotation><\/semantics><\/math>4&times;2&minus;9=0<\/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<h3 class=\"wp-block-heading\">4. Highest power in a quadratic equation is<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A. 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">B. 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">C. 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">D. 5<\/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 a quadratic equation?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A quadratic equation is an equation of degree 2 and is written in the form:<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><mtext>&nbsp;<\/mtext><mi>a<\/mi><mo mathvariant=\"normal\">&ne;<\/mo><mn>0<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">ax^2+bx+c=0,\\ a\\neq0<\/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\">Q2. Why should equations be simplified first?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Some equations may appear quadratic or non-quadratic until simplified. Simplification helps identify the correct degree.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q3. Can a quadratic equation have only one solution?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Yes. It can have two equal real roots when the discriminant is zero.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<h3 class=\"wp-block-heading\">Q4. What is the standard form?<\/h3>\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><\/mrow><annotation encoding=\"application\/x-tex\">ax^2+bx+c=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\">Q5. Which chapter follows Exercise 4.1?<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Exercise 4.2, where students solve quadratic equations using <strong>factorisation<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\">\n\n\n\n<p class=\"wp-block-paragraph\">&#128216; <strong>Found these Exercise 4.1 solutions helpful?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Explore more <strong>NCERT Class 10 Maths Solutions<\/strong>, detailed explanations, chapter-wise notes, MCQs, previous year questions, and exam preparation resources only at <strong><a href=\"http:\/\/www.mymockmate.com\">www.mymockmate.com<\/a><\/strong>. Learn smarter, practice better, and score higher in your CBSE examinations.<\/p>\n<div class=\"pdfprnt-buttons pdfprnt-buttons-post pdfprnt-top-bottom-right\"><a href=\"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5686?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\">11<\/span><\/div><div class=\"mymoc-bottom mymoc-entity-placement\" id=\"mymoc-2999341517\"><div id=\"mymoc-2710358100\"><a href=\"https:\/\/amzn.to\/4fDWGbw\" aria-label=\"smartwatch\"><img src=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png\" alt=\"\" srcset=\"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch.png 1717w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-300x71.png 300w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1024x243.png 1024w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-768x182.png 768w, https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/smartwatch-1536x364.png 1536w\" sizes=\"(max-width: 1717px) 100vw, 1717px\" width=\"1717\" height=\"407\"><\/a><\/div><\/div>","protected":false},"excerpt":{"rendered":"<p> 11 Short Introduction Exercise 4.1 introduces students to Quadratic Equations, one of the most important topics in Class 10 Mathematics. In this exercise, students&#8230;<\/p>\n","protected":false},"author":1,"featured_media":5698,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"footnotes":""},"categories":[10,5],"tags":[48,3595,3598,3593,3596,3600,3599,3597,3594],"class_list":["post-5686","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-maths-class-10","category-class-10","tag-cbse-class-10-maths","tag-chapter-4-maths-solutions","tag-exercise-4-1-answers","tag-ncert-class-10-maths-exercise-4-1-solutions","tag-ncert-maths-class-10-chapter-4","tag-ncert-solutions-2026","tag-quadratic-equation-examples","tag-quadratic-equation-questions","tag-quadratic-equations-exercise-4-1"],"featured_image_src":"https:\/\/mymockmate.com\/notes\/wp-content\/uploads\/2026\/06\/NCERT-Class-10-Maths-Exercise-4.1-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\/5686","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=5686"}],"version-history":[{"count":21,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5686\/revisions"}],"predecessor-version":[{"id":5730,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/5686\/revisions\/5730"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/5698"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=5686"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=5686"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=5686"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}