{"id":237212,"date":"2025-06-17T04:55:23","date_gmt":"2025-06-17T04:55:23","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=237212"},"modified":"2025-06-17T04:55:25","modified_gmt":"2025-06-17T04:55:25","slug":"equation-that-has-no-real-solution","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/17\/equation-that-has-no-real-solution\/","title":{"rendered":"Equation that has no real solution"},"content":{"rendered":"\n<p>Equation that has no real solution: Select the quadratic 9x^2 &#8211; 25x + 30 = 0 9x^2 &#8211; 30x + 25 = 0 9x^2 + 30x + 25 = 0<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/image-612.png\" alt=\"\" class=\"wp-image-237213\"\/><\/figure>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-0-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The quadratic equation that has no real solution is 9&#215;2\u221225x+30=09x^2 &#8211; 25x + 30 = 0.<\/p>\n\n\n\n<p>To determine which equation has no real solution, we use the discriminant formula from the quadratic equation, which is given by:<\/p>\n\n\n\n<p>\u0394=b2\u22124ac\\Delta = b^2 &#8211; 4ac<\/p>\n\n\n\n<p>where aa, bb, and cc are the coefficients from the equation ax2+bx+c=0ax^2 + bx + c = 0. If the discriminant is negative, the quadratic equation has no real solution.<\/p>\n\n\n\n<p>For 9&#215;2\u221225x+30=09x^2 &#8211; 25x + 30 = 0:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>a=9a = 9<\/li>\n\n\n\n<li>b=\u221225b = -25<\/li>\n\n\n\n<li>c=30c = 30<\/li>\n<\/ul>\n\n\n\n<p>The discriminant calculation is:<\/p>\n\n\n\n<p>(\u221225)2\u22124(9)(30)=625\u22121080=\u2212455(-25)^2 &#8211; 4(9)(30) = 625 &#8211; 1080 = -455<\/p>\n\n\n\n<p>Since the discriminant is negative, the equation has no real solution.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<p>Quadratic equations can have real or complex solutions depending on their discriminant. The discriminant is a key factor in the quadratic formula:<\/p>\n\n\n\n<p>x=\u2212b\u00b1b2\u22124ac2ax = \\frac{-b \\pm \\sqrt{b^2 &#8211; 4ac}}{2a}<\/p>\n\n\n\n<p>The value under the square root, b2\u22124acb^2 &#8211; 4ac, determines the nature of the roots:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If the discriminant is positive, the equation has two distinct real solutions.<\/li>\n\n\n\n<li>If the discriminant is zero, the equation has one real solution.<\/li>\n\n\n\n<li>If the discriminant is negative, the equation has no real solutions and instead yields complex numbers.<\/li>\n<\/ul>\n\n\n\n<p>For the given equations, only 9&#215;2\u221225x+30=09x^2 &#8211; 25x + 30 = 0 has a negative discriminant, making it the correct answer. This means the quadratic expression does not cross the x-axis when plotted, reinforcing the fact that it has no real roots.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner5-678.jpeg\" alt=\"\" class=\"wp-image-237214\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Equation that has no real solution: Select the quadratic 9x^2 &#8211; 25x + 30 = 0 9x^2 &#8211; 30x + 25 = 0 9x^2 + 30x + 25 = 0 The Correct Answer and Explanation is: The quadratic equation that has no real solution is 9&#215;2\u221225x+30=09x^2 &#8211; 25x + 30 = 0. To determine which [&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-237212","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237212","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=237212"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/237212\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=237212"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=237212"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=237212"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}