{"id":1603,"date":"2026-05-19T14:30:45","date_gmt":"2026-05-19T14:30:45","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1603"},"modified":"2026-05-19T14:30:47","modified_gmt":"2026-05-19T14:30:47","slug":"class-10-maths-exercise-2-2-solutions-relationship-between-zeroes-and-coefficients","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-2-solutions-relationship-between-zeroes-and-coefficients\/","title":{"rendered":"Class 10 Maths Exercise 2.2 Solutions | Relationship Between Zeroes and Coefficients"},"content":{"rendered":"\n
\n\n\n\n

Short Intro<\/h1>\n\n\n\n

In this post, students can find complete step-by-step solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.2 based on the latest NCERT syllabus. This exercise explains the relationship between zeroes and coefficients of quadratic polynomials in a simple and exam-oriented format.<\/p>\n\n\n\n

Exercise 2.2 focuses on finding zeroes and verifying relationships between zeroes and coefficients of polynomials.<\/p>\n\n\n\n

\n\n\n\n

Quick Information Box<\/h1>\n\n\n\n
Item<\/th>Details<\/th><\/tr><\/thead>
Board<\/td>CBSE<\/td><\/tr>
Class<\/td>10<\/td><\/tr>
Subject<\/td>Maths<\/td><\/tr>
Chapter<\/td>Polynomials<\/td><\/tr>
Exercise<\/td>2.2<\/td><\/tr>
Main Topic<\/td>Relationship Between Zeroes & Coefficients<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n
\n\n\n\n

Concepts Used (Topics Covered)<\/h1>\n\n\n\n
    \n
  • Zeroes of Polynomial<\/li>\n\n\n\n
  • Quadratic Polynomial<\/li>\n\n\n\n
  • Sum of Zeroes<\/li>\n\n\n\n
  • Product of Zeroes<\/li>\n\n\n\n
  • Relationship Between Zeroes and Coefficients<\/li>\n\n\n\n
  • Factorisation Method<\/li>\n<\/ul>\n\n\n\n

    The chapter explains how zeroes of quadratic polynomials are related to coefficients.<\/p>\n\n\n\n

    \n\n\n\n

    Important Formulas<\/h1>\n\n\n\n

    General Quadratic Polynomial<\/h2>\n\n\n\n

    a<\/mi>x<\/mi>2<\/mn><\/msup>+<\/mo>b<\/mi>x<\/mi>+<\/mo>c<\/mi><\/mrow>ax^2+bx+c<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    \n\n\n\n

    Sum of Zeroes<\/h2>\n\n\n\n

    \u03b1<\/mi>+<\/mo>\u03b2<\/mi>=<\/mo>\u2212<\/mo>b<\/mi>a<\/mi><\/mfrac><\/mrow>\\alpha+\\beta=-\\frac{b}{a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    \n\n\n\n

    Product of Zeroes<\/h2>\n\n\n\n

    \u03b1<\/mi>\u03b2<\/mi>=<\/mo>c<\/mi>a<\/mi><\/mfrac><\/mrow>\\alpha\\beta=\\frac{c}{a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    \n\n\n\n

    Questions & Step-by-step Solutions<\/h1>\n\n\n\n

    Question 1<\/h1>\n\n\n\n

    Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and coefficients.<\/h2>\n\n\n\n
    \n\n\n\n

    (i) x\u00b2 \u2212 2x \u2212 8<\/h2>\n\n\n\n

    Solution<\/h3>\n\n\n\n

    Factorising:<\/p>\n\n\n\n

    x\u00b2 \u2212 2x \u2212 8 = (x \u2212 4)(x + 2)<\/code><\/pre>\n\n\n\n
    Zeroes:<\/p>\n\n\n\n
    4 and \u22122<\/code><\/pre>\n\n\n\n
    Verification:<\/p>\n\n\n\n
    Sum of zeroes:<\/p>\n\n\n\n
    4 + (\u22122) = 2<\/code><\/pre>\n\n\n\n
    Using formula:<\/p>\n\n\n\n
    \u2212b\/a = \u2212(\u22122)\/1 = 2<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    Product of zeroes:<\/p>\n\n\n\n
    4 \u00d7 (\u22122) = \u22128<\/code><\/pre>\n\n\n\n
    Using formula:<\/p>\n\n\n\n
    c\/a = \u22128\/1 = \u22128<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    \n\n\n\n
    (ii) x\u00b2 \u2212 7x + 12<\/h2>\n\n\n\n
    Solution<\/h3>\n\n\n\n
    Factorising:<\/p>\n\n\n\n
    x\u00b2 \u2212 7x + 12 = (x \u2212 3)(x \u2212 4)<\/code><\/pre>\n\n\n\n
    Zeroes:<\/p>\n\n\n\n
    3 and 4<\/code><\/pre>\n\n\n\n
    Verification:<\/p>\n\n\n\n
    Sum:<\/p>\n\n\n\n
    3 + 4 = 7<\/code><\/pre>\n\n\n\n
    \u2212b\/a = \u2212(\u22127)\/1 = 7<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    Product:<\/p>\n\n\n\n
    3 \u00d7 4 = 12<\/code><\/pre>\n\n\n\n
    c\/a = 12\/1 = 12<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    \n\n\n\n
    (iii) 6x\u00b2 \u2212 3 \u2212 7x<\/h2>\n\n\n\n
    Solution<\/h3>\n\n\n\n
    Rearranging:<\/p>\n\n\n\n
    6x\u00b2 \u2212 7x \u2212 3<\/code><\/pre>\n\n\n\n
    Factorising:<\/p>\n\n\n\n
    = (3x + 1)(2x \u2212 3)<\/code><\/pre>\n\n\n\n
    Zeroes:<\/p>\n\n\n\n
    \u22121\/3 and 3\/2<\/code><\/pre>\n\n\n\n
    Verification:<\/p>\n\n\n\n
    Sum:<\/p>\n\n\n\n
    \u22121\/3 + 3\/2
    = (\u22122 + 9)\/6
    = 7\/6<\/code><\/pre>\n\n\n\n
    Formula:<\/p>\n\n\n\n
    \u2212b\/a = \u2212(\u22127)\/6 = 7\/6<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    Product:<\/p>\n\n\n\n
    (\u22121\/3)(3\/2) = \u22121\/2<\/code><\/pre>\n\n\n\n
    Formula:<\/p>\n\n\n\n
    c\/a = \u22123\/6 = \u22121\/2<\/code><\/pre>\n\n\n\n
    Verified.<\/p>\n\n\n\n
    \n\n\n\n
    Question 2<\/h1>\n\n\n\n
    Find a quadratic polynomial whose zeroes are:<\/h2>\n\n\n\n
    \n\n\n\n
    (i) 2 and \u22123<\/h2>\n\n\n\n
    Solution<\/h3>\n\n\n\n
    Polynomial:<\/p>\n\n\n\n
    x<\/mi>2<\/mn><\/msup>\u2212<\/mo>(<\/mo>\u03b1<\/mi>+<\/mo>\u03b2<\/mi>)<\/mo>x<\/mi>+<\/mo>\u03b1<\/mi>\u03b2<\/mi><\/mrow>x^2-(\\alpha+\\beta)x+\\alpha\\beta<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
    Substituting values:<\/p>\n\n\n\n
    x\u00b2 \u2212 (2 \u2212 3)x + (2)(\u22123)<\/code><\/pre>\n\n\n\n
    x\u00b2 + x \u2212 6<\/code><\/pre>\n\n\n\n
    Final Answer:<\/p>\n\n\n\n
    x\u00b2 + x \u2212 6<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    (ii) \u221a2 and \u2212\u221a2<\/h2>\n\n\n\n
    Solution<\/h3>\n\n\n\n
    Sum:<\/p>\n\n\n\n
    \u221a2 + (\u2212\u221a2) = 0<\/code><\/pre>\n\n\n\n
    Product:<\/p>\n\n\n\n
    \u221a2 \u00d7 (\u2212\u221a2) = \u22122<\/code><\/pre>\n\n\n\n
    Polynomial:<\/p>\n\n\n\n
    x\u00b2 \u2212 0x \u2212 2<\/code><\/pre>\n\n\n\n
    x\u00b2 \u2212 2<\/code><\/pre>\n\n\n\n
    Final Answer:<\/p>\n\n\n\n
    x\u00b2 \u2212 2<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    (iii) \u221a3 and 1\/\u221a3<\/h2>\n\n\n\n
    Solution<\/h3>\n\n\n\n
    Sum:<\/p>\n\n\n\n
    \u221a3 + 1\/\u221a3<\/code><\/pre>\n\n\n\n
    Taking LCM:<\/p>\n\n\n\n
    = (3 + 1)\/\u221a3
    = 4\/\u221a3<\/code><\/pre>\n\n\n\n
    Product:<\/p>\n\n\n\n
    \u221a3 \u00d7 1\/\u221a3 = 1<\/code><\/pre>\n\n\n\n
    Polynomial:<\/p>\n\n\n\n
    x\u00b2 \u2212 (4\/\u221a3)x + 1<\/code><\/pre>\n\n\n\n
    Multiplying by \u221a3:<\/p>\n\n\n\n
    \u221a3x\u00b2 \u2212 4x + \u221a3<\/code><\/pre>\n\n\n\n
    Final Answer:<\/p>\n\n\n\n
    \u221a3x\u00b2 \u2212 4x + \u221a3<\/code><\/pre>\n\n\n\n
    \n\n\n\n
    Common Mistakes<\/h1>\n\n\n\n
      \n
    • Wrong sign in sum formula<\/li>\n\n\n\n
    • Incorrect factorisation<\/li>\n\n\n\n
    • Forgetting to simplify fractions<\/li>\n\n\n\n
    • Confusing product and sum formulas<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n
      Exam Tips<\/h1>\n\n\n\n
        \n
      • Learn formulas properly.<\/li>\n\n\n\n
      • Verify answers carefully.<\/li>\n\n\n\n
      • Always write factorisation steps.<\/li>\n\n\n\n
      • Practice sign handling regularly.<\/li>\n<\/ul>\n\n\n\n
        \n\n\n\n
        Practice MCQs<\/h1>\n\n\n\n
        MCQ 1<\/h2>\n\n\n\n
        For polynomial ax\u00b2 + bx + c:<\/p>\n\n\n\n
        \u03b1 + \u03b2 equals:<\/p>\n\n\n\n
        A. c\/a
        B. \u2212b\/a
        C. b\/a
        D. \u2212c\/a<\/p>\n\n\n\n
        Answer:<\/p>\n\n\n\n
        B. \u2212b\/a<\/code><\/pre>\n\n\n\n
        \n\n\n\n
        MCQ 2<\/h2>\n\n\n\n
        If zeroes are 2 and 3, product is:<\/p>\n\n\n\n
        A. 5
        B. 6
        C. 1
        D. 0<\/p>\n\n\n\n
        Answer:<\/p>\n\n\n\n
        B. 6<\/code><\/pre>\n\n\n\n
        \n\n\n\n
        MCQ 3<\/h2>\n\n\n\n
        A quadratic polynomial has:<\/p>\n\n\n\n
        A. 1 zero
        B. 2 zeroes
        C. 3 zeroes
        D. Infinite zeroes<\/p>\n\n\n\n
        Answer:<\/p>\n\n\n\n
        B. 2 zeroes<\/code><\/pre>\n\n\n\n
        \n\n\n\n
        MCQ 4<\/h2>\n\n\n\n
        For x\u00b2 \u2212 5x + 6, sum of zeroes is:<\/p>\n\n\n\n
        A. 5
        B. \u22125
        C. 6
        D. \u22126<\/p>\n\n\n\n
        Answer:<\/p>\n\n\n\n
        A. 5<\/code><\/pre>\n\n\n\n
        \n\n\n\n
        FAQ Section<\/h1>\n\n\n\n
        What is the relationship between zeroes and coefficients?<\/h2>\n\n\n\n
        For ax\u00b2 + bx + c:<\/p>\n\n\n\n
        \u03b1<\/mi>+<\/mo>\u03b2<\/mi>=<\/mo>\u2212<\/mo>b<\/mi>a<\/mi><\/mfrac><\/mrow>\\alpha+\\beta=-\\frac{b}{a}<\/annotation><\/semantics><\/math>\u200b<\/p>\n\n\n\n
        and<\/p>\n\n\n\n
        \u03b1<\/mi>\u03b2<\/mi>=<\/mo>c<\/mi>a<\/mi><\/mfrac><\/mrow>\\alpha\\beta=\\frac{c}{a}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n
        \n\n\n\n
        Why is Exercise 2.2 important?<\/h2>\n\n\n\n
        It forms the base for quadratic equations and board exam questions.<\/p>\n\n\n\n
        \n\n\n\n
        Can quadratic polynomials have irrational zeroes?<\/h2>\n\n\n\n
        Yes, quadratic polynomials can have irrational zeroes.<\/p>\n\n\n\n
        \n\n\n\n
        Which method is mostly used in Exercise 2.2?<\/h2>\n\n\n\n
        Factorisation method.<\/p>\n\n\n\n
        \n\n\n\n
        \ud83d\udcd8 Improve Your Maths Preparation with MyMockMate!<\/p>\n\n\n\n
        \u2705 Practice Chapter-wise Mock Tests
        \u2705 Solve Important MCQs
        \u2705 Download NCERT Notes PDF
        \u2705 Get Instant Performance Analysis
        \u2705 Prepare Smarter for Board Exams<\/p>\n\n\n\n
        Start learning now on MyMockMate.<\/p>\n\n\n\n
        \n\n\n\n
        <\/p>\n\n    
        \n\n\t\t\n        
          \n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"
          Short Intro In this post, students can find complete step-by-step solutions for Class 10 Maths Chapter 2 Polynomials<\/p>\n","protected":false},"author":1,"featured_media":1604,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_angie_page":false,"_surecart_dashboard_logo_width":"180px","_surecart_dashboard_show_logo":true,"_surecart_dashboard_navigation_orders":true,"_surecart_dashboard_navigation_invoices":true,"_surecart_dashboard_navigation_subscriptions":true,"_surecart_dashboard_navigation_downloads":true,"_surecart_dashboard_navigation_billing":true,"_surecart_dashboard_navigation_account":true,"postBodyCss":"","postBodyMargin":[],"postBodyPadding":[],"postBodyBackground":{"backgroundType":"classic","gradient":""},"page_builder":"","footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[24],"tags":[48,74,44,83,97,92,96,89,91,53,47,98,84,77,95,87,93,94,80],"class_list":["post-1603","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-polynomials","tag-cbse-class-10-maths","tag-cbse-maths-notes","tag-class-10-maths","tag-class-10-maths-chapter-2","tag-exercise-2-2-ncert-solutions","tag-exercise-2-2-solutions","tag-factorisation-method","tag-maths-board-exam-preparation","tag-maths-chapter-2-solutions","tag-ncert-maths-solutions","tag-ncert-solutions","tag-polynomial-formula","tag-polynomial-questions-answers","tag-polynomials","tag-product-of-zeroes","tag-quadratic-polynomial","tag-relationship-between-zeroes-and-coefficients","tag-sum-of-zeroes","tag-zeroes-of-polynomial"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1603","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=1603"}],"version-history":[{"count":1,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1603\/revisions"}],"predecessor-version":[{"id":1605,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1603\/revisions\/1605"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1604"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1603"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1603"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1603"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}