{"id":169008,"date":"2024-11-19T03:54:27","date_gmt":"2024-11-19T03:54:27","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=169008"},"modified":"2024-11-19T03:54:29","modified_gmt":"2024-11-19T03:54:29","slug":"the-solution-to-3x2-12x-24-0-is","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/11\/19\/the-solution-to-3x2-12x-24-0-is\/","title":{"rendered":"The solution to 3&#215;2 \u2013 12x 24 = 0 is"},"content":{"rendered":"\n<p>The solution to 3&#215;2 \u2013 12x 24 = 0 is<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>The equation (3x^2 &#8211; 12x + 24 = 0) is a quadratic equation. To solve it, we\u2019ll follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">1. Simplify the Equation<\/h3>\n\n\n\n<p>Divide the entire equation by 3 to simplify:<br>[<br>x^2 &#8211; 4x + 8 = 0<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. Calculate the Discriminant ((\\Delta))<\/h3>\n\n\n\n<p>The discriminant of a quadratic equation (ax^2 + bx + c = 0) is given by:<br>[<br>\\Delta = b^2 &#8211; 4ac<br>]<br>Here, (a = 1), (b = -4), and (c = 8). Substituting:<br>[<br>\\Delta = (-4)^2 &#8211; 4(1)(8) = 16 &#8211; 32 = -16<br>]<br>Since the discriminant is negative ((\\Delta &lt; 0)), the equation has <strong>no real solutions<\/strong>, only <strong>complex solutions<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">3. Solve Using the Quadratic Formula<\/h3>\n\n\n\n<p>The quadratic formula is:<br>[<br>x = \\frac{-b \\pm \\sqrt{\\Delta}}{2a}<br>]<br>Substitute the values of (a), (b), and (\\Delta):<br>[<br>x = \\frac{-(-4) \\pm \\sqrt{-16}}{2(1)} = \\frac{4 \\pm \\sqrt{-16}}{2} = \\frac{4 \\pm 4i}{2}<br>]<br>Simplify:<br>[<br>x = 2 \\pm 2i<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer:<\/h3>\n\n\n\n<p>The solutions are:<br>[<br>x = 2 + 2i \\quad \\text{and} \\quad x = 2 &#8211; 2i<br>]<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>The quadratic equation represents a parabola.<\/li>\n\n\n\n<li>A negative discriminant means the parabola does not intersect the (x)-axis, resulting in complex solutions.<\/li>\n\n\n\n<li>Complex solutions include both a real part (2) and an imaginary part ((\\pm 2i)).<\/li>\n\n\n\n<li>Solving with the quadratic formula ensures we account for all possible roots, including complex numbers. These roots represent solutions in the complex plane rather than on the real number line.<\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"<p>The solution to 3&#215;2 \u2013 12x 24 = 0 is The Correct Answer and Explanation is : The equation (3x^2 &#8211; 12x + 24 = 0) is a quadratic equation. To solve it, we\u2019ll follow these steps: 1. Simplify the Equation Divide the entire equation by 3 to simplify:[x^2 &#8211; 4x + 8 = 0] [&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-169008","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169008","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=169008"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/169008\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=169008"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=169008"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=169008"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}