{"id":158177,"date":"2024-10-24T13:50:16","date_gmt":"2024-10-24T13:50:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=158177"},"modified":"2024-10-24T13:50:18","modified_gmt":"2024-10-24T13:50:18","slug":"which-are-the-solutions-of-x%c2%b2-11x-4","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/24\/which-are-the-solutions-of-x%c2%b2-11x-4\/","title":{"rendered":"Which are the solutions of x\u00b2 = -11x + 4"},"content":{"rendered":"\n<p>Which are the solutions of x\u00b2 = -11x + 4?<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To solve the quadratic equation ( x^2 = -11x + 4 ), we first rearrange it into standard form. This involves moving all terms to one side of the equation:<\/p>\n\n\n\n<p>[<br>x^2 + 11x &#8211; 4 = 0<br>]<\/p>\n\n\n\n<p>Now, we will apply the quadratic formula, which is given by:<\/p>\n\n\n\n<p>[<br>x = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}<br>]<\/p>\n\n\n\n<p>In our equation, the coefficients are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( a = 1 )<\/li>\n\n\n\n<li>( b = 11 )<\/li>\n\n\n\n<li>( c = -4 )<\/li>\n<\/ul>\n\n\n\n<p>Next, we will calculate the discriminant ( b^2 &#8211; 4ac ):<\/p>\n\n\n\n<p>[<br>b^2 &#8211; 4ac = 11^2 &#8211; 4 \\cdot 1 \\cdot (-4) = 121 + 16 = 137<br>]<\/p>\n\n\n\n<p>The discriminant is ( 137 ), which is a positive number. This indicates that there are two distinct real solutions to the equation. Now we can substitute the values into the quadratic formula:<\/p>\n\n\n\n<p>[<br>x = \\frac{-11 \\pm \\sqrt{137}}{2 \\cdot 1} = \\frac{-11 \\pm \\sqrt{137}}{2}<br>]<\/p>\n\n\n\n<p>Now, let&#8217;s calculate the two solutions:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>First solution:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>[<br>x_1 = \\frac{-11 + \\sqrt{137}}{2}<br>]<\/p>\n\n\n\n<ol start=\"2\" class=\"wp-block-list\">\n<li><strong>Second solution:<\/strong><\/li>\n<\/ol>\n\n\n\n<p>[<br>x_2 = \\frac{-11 &#8211; \\sqrt{137}}{2}<br>]<\/p>\n\n\n\n<p>These two expressions represent the solutions to the equation ( x^2 + 11x &#8211; 4 = 0 ).<\/p>\n\n\n\n<p>To summarize, the solutions to the quadratic equation ( x^2 = -11x + 4 ) are:<\/p>\n\n\n\n<p>[<br>x = \\frac{-11 + \\sqrt{137}}{2} \\quad \\text{and} \\quad x = \\frac{-11 &#8211; \\sqrt{137}}{2}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>Using the quadratic formula, we derived two distinct solutions for the equation. The presence of a positive discriminant confirms that both solutions are real and distinct, allowing for effective analysis of the equation&#8217;s roots. The solutions can further be evaluated numerically if required for practical applications, but in symbolic form, they provide precise information about the roots of the quadratic equation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Which are the solutions of x\u00b2 = -11x + 4? The Correct Answer and Explanation is: To solve the quadratic equation ( x^2 = -11x + 4 ), we first rearrange it into standard form. This involves moving all terms to one side of the equation: [x^2 + 11x &#8211; 4 = 0] Now, we [&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-158177","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158177","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=158177"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/158177\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=158177"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=158177"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=158177"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}