{"id":266878,"date":"2025-07-23T07:56:16","date_gmt":"2025-07-23T07:56:16","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=266878"},"modified":"2025-07-23T07:56:18","modified_gmt":"2025-07-23T07:56:18","slug":"3x2-2x-5-0","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/23\/3x2-2x-5-0\/","title":{"rendered":"-3x^2 + 2x &#8211; 5 = 0"},"content":{"rendered":"\n<p>-3x^2 + 2x &#8211; 5 = 0<\/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>To solve the quadratic equation \u22123&#215;2+2x\u22125=0-3x^2 + 2x &#8211; 5 = 0\u22123&#215;2+2x\u22125=0, we can use the <strong>quadratic formula<\/strong>, which is given by:x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b<\/p>\n\n\n\n<p>For the equation \u22123&#215;2+2x\u22125=0-3x^2 + 2x &#8211; 5 = 0\u22123&#215;2+2x\u22125=0, we have:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=\u22123a = -3a=\u22123<\/li>\n\n\n\n<li>b=2b = 2b=2<\/li>\n\n\n\n<li>c=\u22125c = -5c=\u22125<\/li>\n<\/ul>\n\n\n\n<p>Now, substitute these values into the quadratic formula:x=\u22122\u00b1(2)2\u22124(\u22123)(\u22125)2(\u22123)x = \\frac{-2 \\pm \\sqrt{(2)^2 &#8211; 4(-3)(-5)}}{2(-3)}x=2(\u22123)\u22122\u00b1(2)2\u22124(\u22123)(\u22125)\u200b\u200b<\/p>\n\n\n\n<p>First, calculate the discriminant (b2\u22124ac)(b^2 &#8211; 4ac)(b2\u22124ac):b2\u22124ac=(2)2\u22124(\u22123)(\u22125)=4\u221260=\u221256b^2 &#8211; 4ac = (2)^2 &#8211; 4(-3)(-5) = 4 &#8211; 60 = -56b2\u22124ac=(2)2\u22124(\u22123)(\u22125)=4\u221260=\u221256<\/p>\n\n\n\n<p>Since the discriminant is negative (\u221256-56\u221256), it means that the equation has <strong>complex solutions<\/strong>. Now, proceed with the solution:x=\u22122\u00b1\u221256\u22126x = \\frac{-2 \\pm \\sqrt{-56}}{-6}x=\u22126\u22122\u00b1\u221256\u200b\u200b<\/p>\n\n\n\n<p>The square root of \u221256-56\u221256 is \u221256=56i=214i \\sqrt{-56} = \\sqrt{56}i = 2\\sqrt{14}i\u221256\u200b=56\u200bi=214\u200bi, where iii is the imaginary unit. Now, substitute this back into the equation:x=\u22122\u00b1214i\u22126x = \\frac{-2 \\pm 2\\sqrt{14}i}{-6}x=\u22126\u22122\u00b1214\u200bi\u200b<\/p>\n\n\n\n<p>Simplify the expression by dividing both terms by \u22126-6\u22126:x=13\u221314i3x = \\frac{1}{3} \\mp \\frac{\\sqrt{14}i}{3}x=31\u200b\u2213314\u200bi\u200b<\/p>\n\n\n\n<p>Thus, the two complex solutions are:x=13+14i3orx=13\u221214i3x = \\frac{1}{3} + \\frac{\\sqrt{14}i}{3} \\quad \\text{or} \\quad x = \\frac{1}{3} &#8211; \\frac{\\sqrt{14}i}{3}x=31\u200b+314\u200bi\u200borx=31\u200b\u2212314\u200bi\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation:<\/h3>\n\n\n\n<p>This equation is quadratic, meaning its solutions can either be real or complex. In this case, the discriminant (b2\u22124ac)(b^2 &#8211; 4ac)(b2\u22124ac) is negative, indicating complex solutions. When you encounter a negative discriminant, the solutions will always involve imaginary numbers.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1628.jpeg\" alt=\"\" class=\"wp-image-266879\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>-3x^2 + 2x &#8211; 5 = 0 The Correct Answer and Explanation is: To solve the quadratic equation \u22123&#215;2+2x\u22125=0-3x^2 + 2x &#8211; 5 = 0\u22123&#215;2+2x\u22125=0, we can use the quadratic formula, which is given by:x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}x=2a\u2212b\u00b1b2\u22124ac\u200b\u200b For the equation \u22123&#215;2+2x\u22125=0-3x^2 + 2x &#8211; 5 = 0\u22123&#215;2+2x\u22125=0, we have: Now, substitute [&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-266878","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266878","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=266878"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/266878\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=266878"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=266878"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=266878"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}