{"id":1589,"date":"2026-05-19T07:34:07","date_gmt":"2026-05-19T07:34:07","guid":{"rendered":"https:\/\/mymockmate.com\/notes\/?p=1589"},"modified":"2026-05-19T07:40:06","modified_gmt":"2026-05-19T07:40:06","slug":"class-10-maths-exercise-2-1-solutions-polynomials-ncert-solutions","status":"publish","type":"post","link":"https:\/\/mymockmate.com\/notes\/class-10-maths-exercise-2-1-solutions-polynomials-ncert-solutions\/","title":{"rendered":"Class 10 Maths Exercise 2.1 Solutions | Polynomials NCERT Solutions"},"content":{"rendered":"\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Short Intro<\/h1>\n\n\n\n<p>In this post, students can find complete step-by-step solutions for Class 10 Maths Chapter 2 Polynomials Exercise 2.1 based on the latest NCERT syllabus. All questions are solved in an easy and exam-oriented format to help students understand the graphical meaning of zeroes of polynomials.<\/p>\n\n\n\n<p>Exercise 2.1 is based on graphs of polynomials and finding the number of zeroes from graphs.<\/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>Item<\/th><th>Details<\/th><\/tr><\/thead><tbody><tr><td>Board<\/td><td>CBSE<\/td><\/tr><tr><td>Class<\/td><td>10<\/td><\/tr><tr><td>Subject<\/td><td>Maths<\/td><\/tr><tr><td>Chapter<\/td><td>Polynomials<\/td><\/tr><tr><td>Exercise<\/td><td>2.1<br><\/td><\/tr><tr><td>Main Topic<\/td><td>Zeroes of Polynomial<\/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>Polynomials<\/li>\n\n\n\n<li>Linear Polynomial<\/li>\n\n\n\n<li>Quadratic Polynomial<\/li>\n\n\n\n<li>Cubic Polynomial<\/li>\n\n\n\n<li>Zeroes of Polynomial<\/li>\n\n\n\n<li>Graphical Representation of Polynomial<\/li>\n<\/ul>\n\n\n\n<p>The exercise explains that zeroes of a polynomial are the x-coordinates where the graph cuts the x-axis.<\/p>\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\">Polynomial Form<\/h2>\n\n\n\n<p>p(x)=ax<sup>n<\/sup>+bx<sup>n\u22121<\/sup>+\u22ef<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Zero of Polynomial<\/h2>\n\n\n\n<p>p(k)=0<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Linear Polynomial<\/h2>\n\n\n\n<p>ax+b<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Quadratic Polynomial<\/h2>\n\n\n\n<p>ax<sup>2<\/sup>+bx+c<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Questions &amp; Step-by-step Solutions<\/h1>\n\n\n\n<h1 class=\"wp-block-heading\">Question 1<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">The graphs of y = p(x) are given below. Find the number of zeroes of p(x) in each case.<\/h2>\n\n\n\n<p>The number of zeroes of a polynomial is equal to the number of times the graph intersects the x-axis.<\/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<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>From the graph, the line is parallel to the x-axis and does not intersect the x-axis.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 0\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(ii)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>From the graph, the curve intersects the x-axis at one point.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 1\n<\/code><\/pre>\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<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>The graph cuts the x-axis at two points.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 2\n<\/code><\/pre>\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<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>The graph intersects the x-axis at two distinct points.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 2\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">(v)<\/h2>\n\n\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>The graph intersects the x-axis at three points.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 3\n<\/code><\/pre>\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<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p>The graph intersects the x-axis at four points.<\/p>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = 4\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">Important Observation<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">Key Rule<\/h2>\n\n\n\n<pre class=\"wp-block-code\"><code>Number of zeroes = Number of points where graph cuts x-axis\n<\/code><\/pre>\n\n\n\n<p>This is the most important concept of Exercise 2.1.<\/p>\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<ul class=\"wp-block-list\">\n<li>Counting touching points incorrectly<\/li>\n\n\n\n<li>Confusing y-axis intersections with x-axis intersections<\/li>\n\n\n\n<li>Missing repeated intersections<\/li>\n\n\n\n<li>Counting turning points as zeroes<\/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 observe only x-axis intersections.<\/li>\n\n\n\n<li>Touching the x-axis also counts as a zero.<\/li>\n\n\n\n<li>Count carefully from left to right.<\/li>\n\n\n\n<li>Practice graph observation questions regularly.<\/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<h2 class=\"wp-block-heading\">MCQ 1<\/h2>\n\n\n\n<p>A polynomial has 3 zeroes if its graph intersects the x-axis:<\/p>\n\n\n\n<p>A. 1 time<br>B. 2 times<br>C. 3 times<br>D. 4 times<\/p>\n\n\n\n<p>Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. 3 times\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 2<\/h2>\n\n\n\n<p>The zeroes of a polynomial are the:<\/p>\n\n\n\n<p>A. y-coordinates<br>B. x-coordinates<br>C. origin points<br>D. slopes<\/p>\n\n\n\n<p>Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. x-coordinates\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 3<\/h2>\n\n\n\n<p>A quadratic polynomial can have at most:<\/p>\n\n\n\n<p>A. 1 zero<br>B. 2 zeroes<br>C. 3 zeroes<br>D. 4 zeroes<\/p>\n\n\n\n<p>Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>B. 2 zeroes\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">MCQ 4<\/h2>\n\n\n\n<p>If the graph does not intersect the x-axis, then the polynomial has:<\/p>\n\n\n\n<p>A. 1 zero<br>B. 2 zeroes<br>C. No zero<br>D. Infinite zeroes<\/p>\n\n\n\n<p>Answer:<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>C. No zero\n<\/code><\/pre>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h1 class=\"wp-block-heading\">FAQ Section<\/h1>\n\n\n\n<h2 class=\"wp-block-heading\">What are zeroes of a polynomial?<\/h2>\n\n\n\n<p>The zeroes of a polynomial are the x-coordinates where the graph intersects the x-axis.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">How many zeroes can a quadratic polynomial have?<\/h2>\n\n\n\n<p>A quadratic polynomial can have at most 2 zeroes.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Can a polynomial have no zeroes?<\/h2>\n\n\n\n<p>Yes, if its graph does not intersect the x-axis.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h2 class=\"wp-block-heading\">Why is Exercise 2.1 important?<\/h2>\n\n\n\n<p>It helps students understand graphical interpretation of polynomials which is important for board exams.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p>\ud83d\udcd8 Improve Your Maths Preparation with MyMockMate!<\/p>\n\n\n\n<p>\u2705 Practice Chapter-wise Mock Tests<br>\u2705 Solve Important MCQs<br>\u2705 Download NCERT Notes PDF<br>\u2705 Get Instant Performance Analysis<br>\u2705 Prepare Smarter for CBSE Board Exams<\/p>\n\n\n\n<p>Start learning now on MyMockMate.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n    <div class=\"xs_social_share_widget xs_share_url after_content \t\tmain_content  wslu-style-1 wslu-share-box-shaped wslu-fill-colored wslu-none wslu-share-horizontal wslu-theme-font-no wslu-main_content\">\n\n\t\t\n        <ul>\n\t\t\t        <\/ul>\n    <\/div> \n","protected":false},"excerpt":{"rendered":"<p>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":1590,"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":[24,1],"tags":[],"class_list":["post-1589","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-polynomials","category-uncategorized"],"jetpack_publicize_connections":[],"_links":{"self":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1589","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=1589"}],"version-history":[{"count":3,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1589\/revisions"}],"predecessor-version":[{"id":1595,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/posts\/1589\/revisions\/1595"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media\/1590"}],"wp:attachment":[{"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/media?parent=1589"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/categories?post=1589"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mymockmate.com\/notes\/wp-json\/wp\/v2\/tags?post=1589"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}