{"id":538,"date":"2023-05-04T10:00:00","date_gmt":"2023-05-04T04:30:00","guid":{"rendered":"https:\/\/www.aplustopper.com\/?p=538"},"modified":"2023-05-05T09:16:45","modified_gmt":"2023-05-05T03:46:45","slug":"solving-a-quadratic-equation-by-factoring","status":"publish","type":"post","link":"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/","title":{"rendered":"Solving A Quadratic Equation By Factoring"},"content":{"rendered":"<h2><strong>Solving A Quadratic Equation By <a href=\"https:\/\/www.aplustopper.com\/types-of-factorization\/\">Factoring<\/a><\/strong><\/h2>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12370\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2.jpg\" alt=\"\" width=\"502\" height=\"277\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2.jpg 502w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2-300x166.jpg 300w\" sizes=\"(max-width: 502px) 100vw, 502px\" \/> <img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12376\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation.jpg\" alt=\"\" width=\"960\" height=\"720\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation.jpg 960w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-300x225.jpg 300w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-768x576.jpg 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12372\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-1.jpg\" alt=\"\" width=\"612\" height=\"394\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-1.jpg 612w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-1-300x193.jpg 300w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-12378\" src=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-1-1.jpg\" alt=\"\" width=\"960\" height=\"720\" srcset=\"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-1-1.jpg 960w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-1-1-300x225.jpg 300w, https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/08\/solve-quadratic-equation-1-1-768x576.jpg 768w\" sizes=\"(max-width: 960px) 100vw, 960px\" \/><\/p>\n<p>Since, 3x<sup>2<\/sup> \u2013 5x + 2 is a quadratic polynomial;<br \/>\n3x<sup>2<\/sup> \u2013 5x + 2 = 0 is a quadratic equation.<br \/>\nAlso,<br \/>\n3x<sup>2<\/sup> \u2013 5x + 2 = 3x<sup>2<\/sup> \u2013 3x \u2013 2x + 2 [Factorising]<br \/>\n= 3x (x \u2013 1) \u2013 2(x \u2013 1)<br \/>\n= (x \u2013 1) (3x \u2013 2)<br \/>\nIn the same way :<br \/>\n3x<sup>2<\/sup> \u2013 5x + 2 = 0 \u00a0 \u21d2 \u00a0 3x<sup>2<\/sup> \u2013 3x \u2013 2x + 2 = 0 \u00a0\u00a0[Factorising L.H.S.]<br \/>\n\u21d2 \u00a0 (x \u2013 1) (3x \u2013 2) = 0<br \/>\ni.e., \u00a0x \u2013 1 = 0 \u00a0 or \u00a0 3x \u2013 2 = 0<br \/>\n\u21d2 \u00a0x = 1 \u00a0 or \u00a0 x = 2\/3<br \/>\nwhich is the solution of given quadratic equation.<br \/>\n<strong>In order to solve the given Quadratic Equation:<\/strong><br \/>\n1. Clear the fractions and brackets, if given.<br \/>\n2. By transfering each term to the left hand side; express the given equation as<br \/>\nax<sup>2\u00a0<\/sup>+ bx + c = 0 \u00a0 or \u00a0 a + bx + cx<sup>2<\/sup> = 0<br \/>\n3. Factorise left hand side of the equation obtained (the right hand side being zero).<br \/>\n4. By putting each factor equal to zero; solve it.<\/p>\n<h2><strong>Solving A Quadratic Equation By Factoring With\u00a0Examples<\/strong><\/h2>\n<p><iframe loading=\"lazy\" width=\"500\" height=\"375\" src=\"https:\/\/www.youtube.com\/embed\/SDe-1lGeS0U?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<p><strong>Example 1:<\/strong> \u00a0 \u00a0Solve \u00a0(i) x<sup>2<\/sup>\u00a0+ 3x \u2013 18 = 0 \u00a0 \u00a0 \u00a0 (ii) (x \u2013 4) (5x + 2) = 0<br \/>\n(iii) 2x<sup>2<\/sup> + ax \u2013 a2 = 0; \u00a0 where \u2018a\u2019 is a real number.<br \/>\n<strong>Sol. \u00a0 \u00a0(i)<\/strong>\u00a0x<sup>2<\/sup>\u00a0+ 3x \u2013 18 = 0<br \/>\n\u21d2 x<sup>2<\/sup> + 6x \u2013 3x \u2013 18 = 0<br \/>\n\u21d2 x(x + 6) \u2013 3(x + 6) = 0<br \/>\ni.e., (x + 6) (x \u2013 3) = 0<br \/>\n\u21d2 x + 6 = 0\u00a0or x \u2013 3 = 0<br \/>\n\u21d2 x = \u2013 6 or x = 3<br \/>\nRoots of the given equation are \u2013 6 and 3<br \/>\n<strong>(ii)<\/strong> (x \u2013 4) (5x + 2) = 0<br \/>\n\u21d2 x \u2013 4 = 0 or 5x + 2 = 0<br \/>\nx = 4 or x = \u2013 2\/5<br \/>\n<strong>(iii)<\/strong> 2x<sup>2<\/sup> + ax \u2013 a<sup>2<\/sup> = 0<br \/>\n\u21d2 2x<sup>2\u00a0<\/sup>+ 2ax \u2013 ax \u2013 a<sup>2\u00a0<\/sup>= 0<br \/>\n\u21d2\u00a02x(x + a) \u2013 a(x + a) = 0<br \/>\ni.e., (x + a) (2x \u2013 a) = 0<br \/>\n\u21d2\u00a0x + a = 0 or 2x \u2013 a = 0<br \/>\n\u21d2\u00a0x = \u2013 a or\u00a0 x = a\/2<\/p>\n<p><strong>Example 2:<\/strong>\u00a0 \u00a0 Solve the following quadratic equations<br \/>\n(i) x<sup>2<\/sup>\u00a0+ 5x = 0 \u00a0 \u00a0 \u00a0 \u00a0 (ii) x<sup>2<\/sup>\u00a0= 3x \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(iii) x<sup>2<\/sup> = 4<br \/>\n<strong>Sol. \u00a0 \u00a0(i) <\/strong>x<sup>2<\/sup>\u00a0+ 5x = 0 \u00a0\u21d2 \u00a0x(x + 5) = 0<br \/>\n\u21d2 \u00a0x = 0 or x + 5 = 0<br \/>\n\u21d2 \u00a0x = 0 or x = \u2013 5<br \/>\n<strong>(ii)\u00a0<\/strong>x<sup>2<\/sup>\u00a0= 3x<br \/>\n\u21d2 x<sup>2<\/sup> \u2013 3x = 0<br \/>\n\u21d2 \u00a0x(x \u2013 3) = 0<br \/>\n\u21d2 \u00a0x = 0 or x = 3<br \/>\n<strong>(iii)<\/strong> x<sup>2<\/sup> = 4<br \/>\n\u21d2 \u00a0x = \u00b1 2<\/p>\n<p><strong>Example 3:<\/strong>\u00a0 \u00a0 \u00a0Solve the following quadratic equations<br \/>\n(i) 7x<sup>2<\/sup> = 8 \u2013 10x \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(ii) 3(x<sup>2<\/sup> \u2013 4) = 5x \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(iii) x(x + 1) + (x + 2) (x + 3) = 42<br \/>\n<strong>Sol. \u00a0 \u00a0(i)\u00a0<\/strong>7x<sup>2<\/sup> = 8 \u2013 10x<br \/>\n\u21d2 7x<sup>2<\/sup> + 10x \u2013 8 = 0<br \/>\n\u21d2 7x<sup>2<\/sup> + 14x \u2013 4x \u2013 8 = 0<br \/>\n\u21d2 7x(x + 2) \u2013 4(x + 2) = 0<br \/>\n\u21d2 (x + 2) (7x \u2013 4) = 0<br \/>\n\u21d2 x + 2 = 0 \u00a0 or \u00a0 7x \u2013 4 = 0<br \/>\n\u21d2 x = \u2013 2 \u00a0 or \u00a0 x = 4\/7<br \/>\n<strong>(ii)\u00a0<\/strong>3(x<sup>2<\/sup> \u2013 4) = 5x<br \/>\n\u21d2 3x<sup>2<\/sup> \u2013 5x \u2013 12 = 0<br \/>\n\u21d2 3x<sup>2<\/sup> \u2013 9x + 4x \u2013\u00ac 12 = 0<br \/>\n\u21d2 3x(x \u2013 3) + 4(x \u2013 3) = 0<br \/>\n\u21d2 (x \u2013 3) (3x + 4) = 0<br \/>\n\u21d2 x \u2013 3 = 0 \u00a0 or \u00a0 3x + 4 = 0<br \/>\n\u21d2 x = 3 \u00a0 or \u00a0 x = \u20134\/3<br \/>\n<strong>(iii)\u00a0<\/strong>x(x + 1) + (x + 2) (x + 3) = 42<br \/>\n\u21d2 x<sup>2<\/sup>\u00a0+ x + x<sup>2<\/sup>\u00a0+ 3x + 2x + 6 \u2013 42 = 0<br \/>\n\u21d2 2x<sup>2<\/sup> + 6x \u2013 36 = 0<br \/>\n\u21d2 x<sup>2<\/sup>\u00a0+ 3x \u2013 18 = 0<br \/>\n\u21d2 x<sup>2<\/sup>\u00a0+ 6x \u2013 3x \u2013 18 = 0<br \/>\n\u21d2 x(x + 6) \u2013 3(x + 6) = 0<br \/>\n\u21d2 (x + 6) (x \u2013 3) = 0<br \/>\n\u21d2 x = \u2013 6 \u00a0 or \u00a0 x = 3<\/p>\n<p><strong>Example 4:<\/strong>\u00a0 \u00a0 \u00a0Solve for x : 12abx<sup>2<\/sup> \u2013 (9a<sup>2<\/sup> \u2013 8b<sup>2<\/sup>) x \u2013 6ab = 0<br \/>\nGiven equation is 12abx<sup>2<\/sup> \u2013 (9a<sup>2<\/sup> \u2013 8b<sup>2<\/sup>) x \u2013 6ab = 0<br \/>\n\u21d2 3ax(4bx \u2013 3a) + 2b(4bx \u2013 3a) = 0<br \/>\n\u21d2 (4bx \u2013 3a) (3ax + 2b) = 0<br \/>\n\u21d2 4bx \u2013 3a = 0 \u00a0 or \u00a0 3ax + 2b = 0<br \/>\n\u21d2 x =3a\/4b \u00a0 or \u00a0 x = \u2013 2b\/3a<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solving A Quadratic Equation By Factoring Since, 3&#215;2 \u2013 5x + 2 is a quadratic polynomial; 3&#215;2 \u2013 5x + 2 = 0 is a quadratic equation. Also, 3&#215;2 \u2013 5x + 2 = 3&#215;2 \u2013 3x \u2013 2x + 2 [Factorising] = 3x (x \u2013 1) \u2013 2(x \u2013 1) = (x \u2013 1) [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[5],"tags":[61,62,64,65,63],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.8 (Yoast SEO v17.8) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Solving A Quadratic Equation By Factoring - A Plus Topper<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solving A Quadratic Equation By Factoring\" \/>\n<meta property=\"og:description\" content=\"Solving A Quadratic Equation By Factoring Since, 3x2 \u2013 5x + 2 is a quadratic polynomial; 3x2 \u2013 5x + 2 = 0 is a quadratic equation. 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Also, 3x2 \u2013 5x + 2 = 3x2 \u2013 3x \u2013 2x + 2 [Factorising] = 3x (x \u2013 1) \u2013 2(x \u2013 1) = (x \u2013 1) [&hellip;]","og_url":"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/","og_site_name":"A Plus Topper","article_publisher":"https:\/\/www.facebook.com\/aplustopper\/","article_published_time":"2023-05-04T04:30:00+00:00","article_modified_time":"2023-05-05T03:46:45+00:00","og_image":[{"url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2.jpg"}],"twitter_card":"summary","twitter_misc":{"Written by":"Veerendra","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Organization","@id":"https:\/\/www.aplustopper.com\/#organization","name":"Aplus Topper","url":"https:\/\/www.aplustopper.com\/","sameAs":["https:\/\/www.facebook.com\/aplustopper\/"],"logo":{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/#logo","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2018\/12\/Aplus_380x90-logo.jpg","width":1585,"height":375,"caption":"Aplus Topper"},"image":{"@id":"https:\/\/www.aplustopper.com\/#logo"}},{"@type":"WebSite","@id":"https:\/\/www.aplustopper.com\/#website","url":"https:\/\/www.aplustopper.com\/","name":"A Plus Topper","description":"Improve your Grades","publisher":{"@id":"https:\/\/www.aplustopper.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/www.aplustopper.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"ImageObject","@id":"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/#primaryimage","inLanguage":"en-US","url":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2.jpg","contentUrl":"https:\/\/www.aplustopper.com\/wp-content\/uploads\/2016\/09\/factorisation-2.jpg","width":502,"height":277},{"@type":"WebPage","@id":"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/#webpage","url":"https:\/\/www.aplustopper.com\/solving-a-quadratic-equation-by-factoring\/","name":"Solving A Quadratic Equation By Factoring - 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