{"id":62552,"date":"2025-05-19T18:12:30","date_gmt":"2025-05-19T12:42:30","guid":{"rendered":"https:\/\/www.oliveboard.in\/blog\/?p=62552"},"modified":"2025-05-19T18:14:23","modified_gmt":"2025-05-19T12:44:23","slug":"quadratic-equation-questions","status":"publish","type":"post","link":"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/","title":{"rendered":"Quadratic Equation Questions for IBPS RRB, PO, and Other Bank Exams"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_77 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of content<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#What_Is_a_Quadratic_Equation\" >What Is a Quadratic Equation?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#Why_Are_Quadratic_Equations_Important_in_Bank_Exams\" >Why Are Quadratic Equations Important in Bank Exams?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#Common_Question_Pattern_for_Quadratic_Equations\" >Common Question Pattern for Quadratic Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#How_to_Solve_Quadratic_Equation_Questions\" >How to Solve Quadratic Equation Questions?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#Tips_and_Tricks_for_Solving_Quadratic_Equations\" >Tips and Tricks for Solving Quadratic Equations<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.oliveboard.in\/blog\/quadratic-equation-questions\/#Solved_Quadratic_Equation_Questions\" >Solved Quadratic Equation Questions<\/a><\/li><\/ul><\/nav><\/div>\n\n<p><strong>Quadratic Equation Questions for IBPS RRB, PO, and Other Bank Exams<\/strong>: In the realm of competitive banking exams like IBPS RRB, IBPS PO, SBI PO, and other similar tests, quantitative aptitude plays a vital role in determining a candidate\u2019s overall score. Among the many topics under this section, quadratic equations is one of the most frequently asked and scored topics.<\/p>\n\n\n\n<p>If prepared well, quadratic equation questions can be solved in under a minute, helping aspirants save crucial time for lengthier problems. Let\u2019s explore this topic in detail, along with practice questions and preparation tips.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"What_Is_a_Quadratic_Equation\"><\/span>What Is a Quadratic Equation?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>A quadratic equation is a second-degree equation of the form: ax2+bx+c=0ax^2 + bx + c = 0ax2+bx+c=0<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li>aaa, bbb, and ccc are real numbers, and<\/li><li>a\u22600a \\neq 0a\ue020=0<\/li><\/ul>\n\n\n\n<p>The equation will always have two roots (real or imaginary), and your task is usually to find and compare these roots with another equation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Why_Are_Quadratic_Equations_Important_in_Bank_Exams\"><\/span>Why Are Quadratic Equations Important in Bank Exams?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>Here\u2019s why you must pay special attention to this topic:<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>High frequency<\/strong>: Almost every banking prelims exam includes 5 questions from quadratic equations.<\/li><li><strong>Time-efficient<\/strong>: Once you master solving them, you can finish all 5 questions in under 3\u20134 minutes.<\/li><li><strong>Conceptually simple<\/strong>: Most questions require factoring or basic comparison.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Common_Question_Pattern_for_Quadratic_Equations\"><\/span>Common Question Pattern for Quadratic Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>In exams, you&#8217;re typically given two quadratic equations, one in variable xxx and one in yyy. You&#8217;re then asked to compare the roots and choose the correct relation: x2+5x+6=0andy2+7y+10=0x^2 + 5x + 6 = 0 \\quad \\text{and} \\quad y^2 + 7y + 10 = 0x2+5x+6=0andy2+7y+10=0<\/p>\n\n\n\n<p>Options are usually<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li>x&gt;yx &gt; yx&gt;y<\/li><li>x&lt;yx &lt; yx&lt;y<\/li><li>x\u2265yx \\ge yx\u2265y<\/li><li>x\u2264yx \\le yx\u2264y<\/li><li>Relationship can&#8217;t be determined<\/li><\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"How_to_Solve_Quadratic_Equation_Questions\"><\/span>How to Solve Quadratic Equation Questions?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p>To solve the quadratic equations step-by-step, follow these steps:<\/p>\n\n\n\n<ol class=\"wp-block-list\"><li><strong>Factor both equations<\/strong>, if possible.<\/li><li><strong>Find the roots<\/strong> of each equation.<\/li><li><strong>Compare<\/strong> every root of xxx with every root of yyy.<\/li><li><strong>Choose the correct option<\/strong> based on the comparison.<\/li><\/ol>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Tips_and_Tricks_for_Solving_Quadratic_Equations\"><\/span>Tips and Tricks for Solving Quadratic Equations<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Always try simple factoring first<\/strong>: most exam questions are designed to be factorable.<\/li><li><strong>Use the quadratic formula<\/strong> only when factoring is hard.<\/li><\/ul>\n\n\n\n<p>x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n<ul class=\"wp-block-list\"><li><strong>Remember identities, such<\/strong> as a2\u2212b2=(a+b)(a\u2212b)a^2 &#8211; b^2 = (a + b)(a &#8211; b)a2\u2212b2=(a+b)(a\u2212b) for quick simplification.<\/li><li><strong>Practice inequality comparisons<\/strong> for root analysis.<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"Solved_Quadratic_Equation_Questions\"><\/span>Solved Quadratic Equation Questions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\n\n\n<p><strong>Q1.<br><\/strong>Solve:<br>x\u00b2 + 7x + 12 = 0<br>y\u00b2 + 9y + 20 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor both equations<\/strong><\/p>\n\n\n\n<p>x\u00b2 + 7x + 12 = (x + 3)(x + 4) \u2192 x = -3, -4<\/p>\n\n\n\n<p>y\u00b2 + 9y + 20 = (y + 4)(y + 5) \u2192 y = -4, -5<\/p>\n\n\n\n<p><strong>Step 2: Compare values<\/strong><\/p>\n\n\n\n<p>x = -3, -4<\/p>\n\n\n\n<p>y = -4, -5<\/p>\n\n\n\n<p><strong>Compare:<\/strong><\/p>\n\n\n\n<p>-3 &gt; -4 and -4 = -4 \u2192 So x \u2265 y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x \u2265 y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q2.<br><\/strong>Solve:<br>x\u00b2 &#8211; 11x + 28 = 0<br>y\u00b2 &#8211; 13y + 42 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor both equations<\/strong><\/p>\n\n\n\n<p>x\u00b2 &#8211; 11x + 28 = (x &#8211; 4)(x &#8211; 7) \u2192 x = 4, 7<\/p>\n\n\n\n<p>y\u00b2 &#8211; 13y + 42 = (y &#8211; 6)(y &#8211; 7) \u2192 y = 6, 7<\/p>\n\n\n\n<p><strong>Step 2: Compare values<\/strong><\/p>\n\n\n\n<p>x = 4, 7<\/p>\n\n\n\n<p>y = 6, 7<\/p>\n\n\n\n<p>4 &lt; 6, 7 = 7 \u2192 x \u2264 y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x \u2264 y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q3<\/strong>.<br>Solve:<br>x\u00b2 &#8211; 6x + 9 = 0<br>y\u00b2 &#8211; 4y + 4 = 0<\/p>\n\n\n\n<p><strong>Step 1: Recognise perfect squares<\/strong><\/p>\n\n\n\n<p>x\u00b2 &#8211; 6x + 9 = (x &#8211; 3)\u00b2 \u2192 x = 3<\/p>\n\n\n\n<p>y\u00b2 &#8211; 4y + 4 = (y &#8211; 2)\u00b2 \u2192 y = 2<\/p>\n\n\n\n<p><strong>Step 2: Compare values<\/strong><\/p>\n\n\n\n<p>x = 3<\/p>\n\n\n\n<p>y = 2<\/p>\n\n\n\n<p>3 &gt; 2<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x &gt; y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q4<\/strong>.<br>Solve:<br>x\u00b2 + 3x &#8211; 10 = 0<br>y\u00b2 + 5y &#8211; 14 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = 2, -5<\/p>\n\n\n\n<p>y = 2, -7<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>One value is equal (x = y = 2), other x &gt; y (-5 &gt; -7)<br>\u2192 Mixed results<\/p>\n\n\n\n<p><strong>Answer<\/strong>: Cannot be determined<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q5.<br><\/strong>Solve:<br>x\u00b2 + 5x + 6 = 0<br>y\u00b2 + 6y + 9 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x\u00b2 + 5x + 6 = (x + 2)(x + 3) \u2192 x = -2, -3<\/p>\n\n\n\n<p>y\u00b2 + 6y + 9 = (y + 3)\u00b2 \u2192 y = -3<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>x = -2, -3<\/p>\n\n\n\n<p>y = -3<br>\u2192 -2 &gt; -3 and -3 = -3 \u2192 x \u2265 y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x \u2265 y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q6.<br><\/strong>Solve:<br>x\u00b2 &#8211; 10x + 21 = 0<br>y\u00b2 &#8211; 7y + 10 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = 3, 7<\/p>\n\n\n\n<p>y = 2, 5<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>3 &gt; 2 and 7 &gt; 5 \u2192 x &gt; y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x &gt; y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q7.<br><\/strong>Solve:<br>x\u00b2 &#8211; 8x + 15 = 0<br>y\u00b2 &#8211; 7y + 12 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = 3, 5<\/p>\n\n\n\n<p>y = 3, 4<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>3 = 3, 5 &gt; 4 \u2192 x \u2265 y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x \u2265 y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q8<\/strong>.<br>Solve:<br>x\u00b2 &#8211; x &#8211; 20 = 0<br>y\u00b2 + 2y &#8211; 24 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = 5, -4<\/p>\n\n\n\n<p>y = 4, -6<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>One x = 5 &gt; y = 4<\/p>\n\n\n\n<p>Other x = -4 &gt; y = -6<br>\u2192 Both x values &gt; y values<\/p>\n\n\n\n<p><strong>Answer<\/strong>: x &gt; y<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q9<\/strong>.<br>Solve:<br>x\u00b2 &#8211; 2x &#8211; 35 = 0<br>y\u00b2 &#8211; 7y + 10 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = 7, -5<\/p>\n\n\n\n<p>y = 2, 5<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>x = 7 &gt; 5, -5 &lt; 2 \u2192 One x &gt; y, one x &lt; y<\/p>\n\n\n\n<p><strong>Answer<\/strong>: Cannot be determined<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Q10<\/strong>.<br>Solve:<br>x\u00b2 + 10x + 24 = 0<br>y\u00b2 + 9y + 20 = 0<\/p>\n\n\n\n<p><strong>Step 1: Factor<\/strong><\/p>\n\n\n\n<p>x = -4, -6<\/p>\n\n\n\n<p>y = -4, -5<\/p>\n\n\n\n<p><strong>Step 2: Compare<\/strong><\/p>\n\n\n\n<p>x = -4, -6<\/p>\n\n\n\n<p>y = -4, -5<br>\u2192 One x = y, one x &lt; y \u2192 mixed<\/p>\n\n\n\n<p><strong>Answer<\/strong>: Cannot be determined<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n<ul class=\"wp-block-latest-posts__list is-grid columns-3 wp-block-latest-posts\"><li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"128\" height=\"84\" src=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2026\/02\/IBPS-SO-Reserve-List.webp\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"IBPS SO 1st Reserve List 2025-26\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ibps-so-reserve-list-link\/\">IBPS SO 1st Reserve List 2025-26 Out, Check Allotment Status<\/a><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"128\" height=\"84\" src=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2026\/02\/IBPS-PO-Reserve-List.webp\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"IBPS PO Reserve List\" style=\"\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/ibps-po-reserve-list-link\/\">IBPS PO 1st Reserve List 2025-26 Out, Check Now<\/a><\/li>\n<li><div class=\"wp-block-latest-posts__featured-image\"><img loading=\"lazy\" decoding=\"async\" width=\"128\" height=\"84\" src=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2023\/01\/SBI-Clerk-Financial-Awareness.png\" class=\"attachment-thumbnail size-thumbnail wp-post-image\" alt=\"SBI Clerk Financial Awareness\" style=\"\" srcset=\"https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2023\/01\/SBI-Clerk-Financial-Awareness.png 730w, https:\/\/www.oliveboard.in\/blog\/wp-content\/uploads\/2023\/01\/SBI-Clerk-Financial-Awareness-150x99.png 150w\" sizes=\"auto, (max-width: 128px) 100vw, 128px\" \/><\/div><a class=\"wp-block-latest-posts__post-title\" href=\"https:\/\/www.oliveboard.in\/blog\/how-to-prepare-for-financial-awareness-in-sbi-clerk-mains\/\">SBI Clerk Banking Awareness Questions &amp; 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Check Eligibility with FREE Live Tool<\/a><\/li>\n<\/ul>\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n","protected":false},"excerpt":{"rendered":"<p>Quadratic Equation Questions for IBPS RRB, PO, and Other Bank Exams: In the realm of competitive banking exams like IBPS<\/p>\n","protected":false},"author":2,"featured_media":217159,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,31,601],"tags":[600,17609],"class_list":["post-62552","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-articles","category-bank-exams","category-other-banking","tag-bank-exams","tag-quadratic-equation-questions","generate-columns","tablet-grid-50","mobile-grid-100","grid-parent","grid-50"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v26.6 (Yoast SEO v26.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Quadratic 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