{"id":10814,"date":"2022-05-30T15:51:38","date_gmt":"2022-05-30T10:21:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10814"},"modified":"2022-05-30T15:51:41","modified_gmt":"2022-05-30T10:21:41","slug":"find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/","title":{"rendered":"Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, &#8211; 7, -14 respectively."},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>Let the cubic polynomial be \\(ax^3 + bx^2 + cx + d\\), and its zeroes be \\(\\alpha\\), \\(\\beta\\) and \\(\\gamma\\).<\/p>\n<p>Then,\u00a0 \\(\\alpha\\) + \\(\\beta\\) + \\(\\gamma\\) = 2 = \\(-(-2)\\over 1\\) = \\(-b\\over a\\)<\/p>\n<p>\\(\\alpha\\)\\(\\beta\\) + \\(\\beta\\)\\(\\gamma\\) +\u00a0\\(\\gamma\\)\\(\\alpha\\) = &#8211; 7 = \\(-7\\over 1\\) = \\(c\\over a\\)<\/p>\n<p>and \\(\\alpha\\)\\(\\beta\\)\\(\\gamma\\) = -14 = \\(-14\\over 1\\) = \\(-d\\over a\\)<\/p>\n<p>If a = 1, then b = -2, c = -7 and d = 14.<\/p>\n<p>So, one cubic polynomial which satisfy the given conditions will be <strong>\\(x^3 &#8211; 7x + 14\\)<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : Let the cubic polynomial be \\(ax^3 + bx^2 + cx + d\\), and its zeroes be \\(\\alpha\\), \\(\\beta\\) and \\(\\gamma\\). Then,\u00a0 \\(\\alpha\\) + \\(\\beta\\) + \\(\\gamma\\) = 2 = \\(-(-2)\\over 1\\) = \\(-b\\over a\\) \\(\\alpha\\)\\(\\beta\\) + \\(\\beta\\)\\(\\gamma\\) +\u00a0\\(\\gamma\\)\\(\\alpha\\) = &#8211; 7 = \\(-7\\over 1\\) = \\(c\\over a\\) and \\(\\alpha\\)\\(\\beta\\)\\(\\gamma\\) = -14 = \\(-14\\over &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/\"> <span class=\"screen-reader-text\">Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, &#8211; 7, -14 respectively.<\/span> Read More &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,910],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, -14 respectively. - Mathemerize<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, - 7, -14 respectively. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : Let the cubic polynomial be (ax^3 + bx^2 + cx + d), and its zeroes be (alpha), (beta) and (gamma). Then,\u00a0 (alpha) + (beta) + (gamma) = 2 = (-(-2)over 1) = (-bover a) (alpha)(beta) + (beta)(gamma) +\u00a0(gamma)(alpha) = &#8211; 7 = (-7over 1) = (cover a) and (alpha)(beta)(gamma) = -14 = (-14over &hellip; Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, &#8211; 7, -14 respectively. Read More &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-05-30T10:21:38+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-30T10:21:41+00:00\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/find-the-cubic-polynomial-with-the-sum-sum-of-the-products-of-its-zeroes-taken-two-at-a-time-and-the-product-of-its-zeroes-as-2-7-14-respectively\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, &#8211; 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Then,\u00a0 (alpha) + (beta) + (gamma) = 2 = (-(-2)over 1) = (-bover a) (alpha)(beta) + (beta)(gamma) +\u00a0(gamma)(alpha) = &#8211; 7 = (-7over 1) = (cover a) and (alpha)(beta)(gamma) = -14 = (-14over &hellip; Find the cubic polynomial with the sum, sum of the products of its zeroes taken two at a time, and the product of its zeroes as 2, &#8211; 7, -14 respectively. 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