{"id":10824,"date":"2022-05-31T13:35:13","date_gmt":"2022-05-31T08:05:13","guid":{"rendered":"https:\/\/mathemerize.com\/?p=10824"},"modified":"2022-05-31T13:35:17","modified_gmt":"2022-05-31T08:05:17","slug":"if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/","title":{"rendered":"If two zeroes of the polynomial \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes."},"content":{"rendered":"

Solution :<\/h2>\n

We have : \\(2 \\pm \\sqrt{3}\\) are two zeroes of the polynomial<\/p>\n

p(x) = \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\)<\/p>\n

Let x = \\(2 \\pm \\sqrt{3}\\),\u00a0 So, x – 2 = \\(\\pm \\sqrt{3}\\)<\/p>\n

Squaring, we get<\/p>\n

\\(x^2 – 4x + 4\\) = 3,\u00a0 \u00a0i.e.\u00a0 \\(x^2 – 4x + 1\\) = 0<\/p>\n

Let us divide p(x) by \\(x^2 – 4x + 1\\) to obtain other zeroes.<\/p>\n

\"polynomial<\/p>\n

\\(\\therefore\\)\u00a0 p(x) = \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\)<\/p>\n

= (\\(x^2 – 4x + 1\\))(\\(x^2 – 2x – 35\\))<\/p>\n

= (\\(x^2 – 4x + 1\\))(\\(x^2 – 7x + 5x – 35\\))<\/p>\n

= (\\(x^2 – 4x + 1\\))(x + 5)(x – 7)<\/p>\n

So, (x+ 5) and (x – 7) are the other factors of p(x).<\/p>\n

\\(\\therefore\\)\u00a0 \u00a0 -5\u00a0 and 7 are other zeroes of the given polynomial<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have : \\(2 \\pm \\sqrt{3}\\) are two zeroes of the polynomial p(x) = \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\) Let x = \\(2 \\pm \\sqrt{3}\\),\u00a0 So, x – 2 = \\(\\pm \\sqrt{3}\\) Squaring, we get \\(x^2 – 4x + 4\\) = 3,\u00a0 \u00a0i.e.\u00a0 \\(x^2 – 4x + 1\\) = …<\/p>\n

If two zeroes of the polynomial \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes.<\/span> Read More »<\/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":"\nIf two zeroes of the polynomial \\(x^4 - 6x^3 - 26x^2 + 138x - 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes. - 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\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"If two zeroes of the polynomial \\(x^4 - 6x^3 - 26x^2 + 138x - 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : We have : (2 pm sqrt{3}) are two zeroes of the polynomial p(x) = (x^4 – 6x^3 – 26x^2 + 138x – 35) Let x = (2 pm sqrt{3}),\u00a0 So, x – 2 = (pm sqrt{3}) Squaring, we get (x^2 – 4x + 4) = 3,\u00a0 \u00a0i.e.\u00a0 (x^2 – 4x + 1) = … If two zeroes of the polynomial (x^4 – 6x^3 – 26x^2 + 138x – 35) are (2 pm sqrt{3}), find other zeroes. Read More »\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2022-05-31T08:05:13+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-05-31T08:05:17+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/05\/polynomial2-4-4-300x129.jpeg\" \/>\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\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"If two zeroes of the polynomial \\\\(x^4 – 6x^3 – 26x^2 + 138x – 35\\\\) are \\\\(2 \\\\pm \\\\sqrt{3}\\\\), find other zeroes.\",\"datePublished\":\"2022-05-31T08:05:13+00:00\",\"dateModified\":\"2022-05-31T08:05:17+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\"},\"wordCount\":125,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Maths Questions\",\"Polynomial Questions\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\",\"url\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\",\"name\":\"If two zeroes of the polynomial \\\\(x^4 - 6x^3 - 26x^2 + 138x - 35\\\\) are \\\\(2 \\\\pm \\\\sqrt{3}\\\\), find other zeroes. - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2022-05-31T08:05:13+00:00\",\"dateModified\":\"2022-05-31T08:05:17+00:00\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"If two zeroes of the polynomial \\\\(x^4 – 6x^3 – 26x^2 + 138x – 35\\\\) are \\\\(2 \\\\pm \\\\sqrt{3}\\\\), find other zeroes.\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"If two zeroes of the polynomial \\(x^4 - 6x^3 - 26x^2 + 138x - 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes. - Mathemerize","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/","og_locale":"en_US","og_type":"article","og_title":"If two zeroes of the polynomial \\(x^4 - 6x^3 - 26x^2 + 138x - 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes. - Mathemerize","og_description":"Solution : We have : (2 pm sqrt{3}) are two zeroes of the polynomial p(x) = (x^4 – 6x^3 – 26x^2 + 138x – 35) Let x = (2 pm sqrt{3}),\u00a0 So, x – 2 = (pm sqrt{3}) Squaring, we get (x^2 – 4x + 4) = 3,\u00a0 \u00a0i.e.\u00a0 (x^2 – 4x + 1) = … If two zeroes of the polynomial (x^4 – 6x^3 – 26x^2 + 138x – 35) are (2 pm sqrt{3}), find other zeroes. Read More »","og_url":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/","og_site_name":"Mathemerize","article_published_time":"2022-05-31T08:05:13+00:00","article_modified_time":"2022-05-31T08:05:17+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2022\/05\/polynomial2-4-4-300x129.jpeg"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"If two zeroes of the polynomial \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes.","datePublished":"2022-05-31T08:05:13+00:00","dateModified":"2022-05-31T08:05:17+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/"},"wordCount":125,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Maths Questions","Polynomial Questions"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/","url":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/","name":"If two zeroes of the polynomial \\(x^4 - 6x^3 - 26x^2 + 138x - 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes. - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2022-05-31T08:05:13+00:00","dateModified":"2022-05-31T08:05:17+00:00","breadcrumb":{"@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/if-two-zeroes-of-the-polynomial-x4-6x3-26x2-138x-35-are-2-pm-sqrt3-find-other-zeroes\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"If two zeroes of the polynomial \\(x^4 – 6x^3 – 26x^2 + 138x – 35\\) are \\(2 \\pm \\sqrt{3}\\), find other zeroes."}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10824"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=10824"}],"version-history":[{"count":1,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10824\/revisions"}],"predecessor-version":[{"id":10826,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/10824\/revisions\/10826"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=10824"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=10824"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=10824"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}