{"id":27936,"date":"2025-06-20T08:01:38","date_gmt":"2025-06-20T08:01:38","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27936"},"modified":"2025-06-20T08:01:40","modified_gmt":"2025-06-20T08:01:40","slug":"find-the-roots-of-x2-4x-5-0-by-factorisation","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/find-the-roots-of-x2-4x-5-0-by-factorisation\/","title":{"rendered":"Find the roots of x2 + 4x &#8211; 5 = 0 by factorisation"},"content":{"rendered":"\n<p>Find the roots of x2 + 4x &#8211; 5 = 0 by factorisation.<br><\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p>To find the roots of the quadratic equation<br><strong>x\u00b2 + 4x \u2212 5 = 0<\/strong><br>by <strong>factorisation<\/strong>, we 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\">\u2705 <strong>Correct Answer:<\/strong><\/h3>\n\n\n\n<p>Factorising:<br><strong>x\u00b2 + 4x \u2212 5 = (x + 5)(x \u2212 1) = 0<\/strong><\/p>\n\n\n\n<p>Setting each factor equal to zero:<br><strong>x + 5 = 0<\/strong> \u2192 <strong>x = \u22125<\/strong><br><strong>x \u2212 1 = 0<\/strong> \u2192 <strong>x = 1<\/strong><\/p>\n\n\n\n<p><strong>\u2234 The roots are x = \u22125 and x = 1.<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">\ud83e\udde0 <strong>300 Words Explanation:<\/strong><\/h3>\n\n\n\n<p>Factorisation is a method used to break a quadratic expression into two binomial expressions whose product gives the original quadratic. The general form of a quadratic is:<br><strong>ax\u00b2 + bx + c = 0<\/strong>, where <strong>a, b, c<\/strong> are constants.<\/p>\n\n\n\n<p>In our equation:<br><strong>x\u00b2 + 4x \u2212 5 = 0<\/strong>,<br>we identify:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>a = 1<\/strong><\/li>\n\n\n\n<li><strong>b = 4<\/strong><\/li>\n\n\n\n<li><strong>c = \u22125<\/strong><\/li>\n<\/ul>\n\n\n\n<p>The goal is to <strong>split the middle term (4x)<\/strong> into two terms whose coefficients multiply to give <strong>a \u00d7 c = 1 \u00d7 (\u22125) = \u22125<\/strong> and add up to <strong>b = 4<\/strong>.<\/p>\n\n\n\n<p>We look for two numbers whose:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Product = \u22125<\/strong><\/li>\n\n\n\n<li><strong>Sum = 4<\/strong><\/li>\n<\/ul>\n\n\n\n<p>These numbers are <strong>5 and \u22121<\/strong>, because:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>5 \u00d7 (\u22121) = \u22125<\/li>\n\n\n\n<li>5 + (\u22121) = 4<\/li>\n<\/ul>\n\n\n\n<p>Now rewrite the equation using these two numbers:<br><strong>x\u00b2 + 5x \u2212 x \u2212 5 = 0<\/strong><\/p>\n\n\n\n<p>Group the terms:<br><strong>(x\u00b2 + 5x) \u2212 (x + 5) = 0<\/strong><\/p>\n\n\n\n<p>Factor each group:<br><strong>x(x + 5) \u22121(x + 5) = 0<\/strong><\/p>\n\n\n\n<p>Now factor the common binomial:<br><strong>(x \u2212 1)(x + 5) = 0<\/strong><\/p>\n\n\n\n<p>Use the <strong>zero product property<\/strong> (if ab = 0, then either a = 0 or b = 0):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>x \u2212 1 = 0 \u2192 x = 1<\/li>\n\n\n\n<li>x + 5 = 0 \u2192 x = \u22125<\/li>\n<\/ul>\n\n\n\n<p>Hence, the equation <strong>x\u00b2 + 4x \u2212 5 = 0<\/strong> has two real roots:<br><strong>x = \u22125 and x = 1<\/strong><\/p>\n\n\n\n<p>This shows that the equation can be solved purely by factoring and applying basic algebraic principles.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the roots of x2 + 4x &#8211; 5 = 0 by factorisation. The correct answer and explanation is: To find the roots of the quadratic equationx\u00b2 + 4x \u2212 5 = 0by factorisation, we follow these steps: \u2705 Correct Answer: Factorising:x\u00b2 + 4x \u2212 5 = (x + 5)(x \u2212 1) = 0 Setting [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27936","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27936","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27936"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27936\/revisions"}],"predecessor-version":[{"id":27941,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27936\/revisions\/27941"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27936"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27936"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27936"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}