{"id":1726,"date":"2012-06-04T22:11:39","date_gmt":"2012-06-04T22:11:39","guid":{"rendered":"http:\/\/schooltutoring.com\/scholarship\/?p=1726"},"modified":"2014-12-02T08:33:44","modified_gmt":"2014-12-02T08:33:44","slug":"framing-a-quadratic-equation","status":"publish","type":"post","link":"https:\/\/schooltutoring.com\/scholarship\/2012\/06\/04\/framing-a-quadratic-equation\/","title":{"rendered":"Framing a Quadratic Equation"},"content":{"rendered":"<p><strong><span style=\"text-decoration: underline\">Quadratic equation:<\/span><\/strong><\/p>\n<p>A quadratic equation is an equation with degree (highest power) 2.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x<sup>2<\/sup> + 5x + 6 = 0;<\/p>\n<p>ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x<sup>2 <\/sup>\u2013 x \u2013 6 = 0.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Root or solution:<\/span><\/strong><\/p>\n<p>A root (a solution) of a quadratic equation is a value which satisfies the equation.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -3 is a root of x<sup>2<\/sup> + 5x + 6 = 0.<\/p>\n<p>iii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 3 is a root of x<sup>2 <\/sup>\u2013 x \u2013 6 = 0.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Factor:<\/span><\/strong><\/p>\n<p>If \u2018a\u2019 is a root of quadratic equation then x-a is a factor to it.<\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>Since 3 is a root of x<sup>2 <\/sup>\u2013 x \u2013 6 = 0, x-3 is a factor to it.<\/p>\n<p><strong><span style=\"text-decoration: underline\">Framing a quadratic equation:<\/span><\/strong><\/p>\n<p>If \u2018a\u2019 and \u2018b\u2019 are the roots of a quadratic equation then x-a and x-b are its corresponding factors.<\/p>\n<p>So, the corresponding equation is,<\/p>\n<p>(x-a)(x-b)=0<\/p>\n<p><strong>x<sup>2<\/sup> \u2013(a+b)x + ab = 0.<\/strong><\/p>\n<p><strong>Example:<\/strong><\/p>\n<p>Frame a quadratic equation with the roots 1 and 2.<\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p>Here a=1 and b=2.<\/p>\n<p>So the corresponding equation is,<\/p>\n<p><strong>x<sup>2<\/sup> \u2013(a+b)x + ab = 0<\/strong><\/p>\n<p>x<sup>2<\/sup> \u2013(1+2)x + 1*2 = 0<\/p>\n<p>x<sup>2<\/sup> \u20133x+2=0.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quadratic equation: A quadratic equation is an equation with degree (highest power) 2. Example: i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x2 + 5x + 6 = 0; ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x2 \u2013 x \u2013 6 = 0. Root or solution: A root (a solution) of a quadratic equation is a value which satisfies the equation. Example: i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 -3 is a root of [&hellip;]<\/p>\n","protected":false},"author":19,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"inline_featured_image":false,"footnotes":""},"categories":[2],"tags":[141,490,907,1093,1215,1505,1713,1857],"class_list":["post-1726","post","type-post","status-publish","format-standard","hentry","category-algebra","tag-arrangement","tag-diagonal","tag-identity","tag-matrix","tag-null","tag-rectangular","tag-square","tag-triangular"],"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/users\/19"}],"replies":[{"embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/comments?post=1726"}],"version-history":[{"count":0,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/posts\/1726\/revisions"}],"wp:attachment":[{"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/media?parent=1726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/categories?post=1726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/schooltutoring.com\/scholarship\/wp-json\/wp\/v2\/tags?post=1726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}