{"id":235479,"date":"2025-06-15T11:59:17","date_gmt":"2025-06-15T11:59:17","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235479"},"modified":"2025-06-15T11:59:45","modified_gmt":"2025-06-15T11:59:45","slug":"ii-8xa%c2%b2-14x-15","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/ii-8xa%c2%b2-14x-15\/","title":{"rendered":"(ii) 8x\u00c2\u00b2 &#8211; 14x &#8211; 15."},"content":{"rendered":"\n<p><br>(ii) 8x\u00c2\u00b2 &#8211; 14x &#8211; 15. Find the zeroes of this quadratic polynomial and verify the relationship between the zeroes and coefficients.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p><strong>Correct Answer:<\/strong><br>Given quadratic polynomial:<br><strong>8x\u00b2 &#8211; 14x &#8211; 15<\/strong><\/p>\n\n\n\n<p><strong>Step 1: Find the zeroes using factorization<\/strong><br>To factor 8x\u00b2 &#8211; 14x &#8211; 15, first find two numbers whose product is:<br><strong>(8)(-15) = -120<\/strong><br>and whose sum is:<br><strong>-14<\/strong><\/p>\n\n\n\n<p>The two numbers are <strong>6 and -20<\/strong> because:<br><strong>6 \u00d7 (-20) = -120<\/strong><br><strong>6 + (-20) = -14<\/strong><\/p>\n\n\n\n<p>Now, split the middle term:<\/p>\n\n\n\n<p><strong>8x\u00b2 + 6x &#8211; 20x &#8211; 15<\/strong><\/p>\n\n\n\n<p>Group terms:<\/p>\n\n\n\n<p><strong>(8x\u00b2 + 6x) &#8211; (20x + 15)<\/strong><\/p>\n\n\n\n<p>Factor each group:<\/p>\n\n\n\n<p><strong>2x(4x + 3) -5(4x + 3)<\/strong><\/p>\n\n\n\n<p>Factor out the common binomial:<\/p>\n\n\n\n<p><strong>(4x + 3)(2x &#8211; 5)<\/strong><\/p>\n\n\n\n<p>Set each factor equal to zero:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>4x + 3 = 0 \u2192 x = -3\/4<\/li>\n\n\n\n<li>2x &#8211; 5 = 0 \u2192 x = 5\/2<\/li>\n<\/ol>\n\n\n\n<p>So, the zeroes of the polynomial are <strong>x = -3\/4<\/strong> and <strong>x = 5\/2<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Step 2: Verify relationship between zeroes and coefficients<\/strong><br>For a quadratic polynomial in the form <strong>ax\u00b2 + bx + c<\/strong>, the relationships are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Sum of zeroes = -b\/a<\/strong><\/li>\n\n\n\n<li><strong>Product of zeroes = c\/a<\/strong><\/li>\n<\/ul>\n\n\n\n<p>From the polynomial 8x\u00b2 &#8211; 14x &#8211; 15:<br>a = 8, b = -14, c = -15<\/p>\n\n\n\n<p><strong>Sum of zeroes:<\/strong><br>(-3\/4) + (5\/2) = (-3 + 10)\/4 = 7\/4<br><strong>-b\/a = -(-14)\/8 = 14\/8 = 7\/4<\/strong> \u2714\ufe0f<\/p>\n\n\n\n<p><strong>Product of zeroes:<\/strong><br>(-3\/4)(5\/2) = -15\/8<br><strong>c\/a = -15\/8<\/strong> \u2714\ufe0f<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Conclusion:<\/strong><br>The zeroes of the quadratic polynomial 8x\u00b2 &#8211; 14x &#8211; 15 are <strong>-3\/4 and 5\/2<\/strong>. These zeroes satisfy the relationships between the sum and product of zeroes and the coefficients, confirming the correctness of the factorization and computation.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-580.jpeg\" alt=\"\" class=\"wp-image-235480\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>(ii) 8x\u00c2\u00b2 &#8211; 14x &#8211; 15. Find the zeroes of this quadratic polynomial and verify the relationship between the zeroes and coefficients. The Correct Answer and Explanation is: Correct Answer:Given quadratic polynomial:8x\u00b2 &#8211; 14x &#8211; 15 Step 1: Find the zeroes using factorizationTo factor 8x\u00b2 &#8211; 14x &#8211; 15, first find two numbers whose product [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-235479","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235479","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=235479"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235479\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235479"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235479"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235479"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}