{"id":6675,"date":"2021-10-19T18:11:02","date_gmt":"2021-10-19T12:41:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6675"},"modified":"2021-11-27T23:30:46","modified_gmt":"2021-11-27T18:00:46","slug":"solve-quadratic-equation-by-factorisation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/solve-quadratic-equation-by-factorisation\/","title":{"rendered":"Solve Quadratic Equation by Factorisation"},"content":{"rendered":"

Here you will learn how to solve quadratic equation by factorisation with examples.<\/p>\n

Let’s begin –<\/p>\n

Solve Quadratic Equation by Factorisation<\/h2>\n
\n

Step 1<\/strong>. Splitting of middle term :<\/p>\n

(i) If the product of a and c = +ac<\/p>\n

then we have to choose two factors ac whose sum is equal to b.<\/p>\n

(ii) If the product of a and c = -ac<\/p>\n

then we have to choose two factors of ac whose difference is equal to b.<\/p>\n

Step 2<\/strong> : Let the factors of \\(ax^2 + bx + c\\) be (dx + e) and (fx + g)<\/p>\n

\\(\\implies\\) (dx + e) (fx + g) = 0<\/p>\n

Either\u00a0 dx + e =\u00a0 or\u00a0 fx + g = 0\u00a0<\/p>\n

\\(\\implies\\)\u00a0 x = -\\(e\\over d\\)\u00a0 \u00a0or\u00a0 \u00a0x = -\\(g\\over f\\)<\/p>\n<\/blockquote>\n

Example<\/strong><\/span> : Solve the equation : \\(2x^2 – 11x + 12\\) = 0.<\/p>\n

Solution<\/span><\/strong> : We have, \\(2x^2 – 11x + 12\\) = 0<\/p>\n

\\(2x^2 – 8x – 3x + 12\\) = 0<\/p>\n

2x (x – 4) – 3 (x – 4) = 0<\/p>\n

(x – 4) (2x – 3) = 0<\/p>\n

\\(\\implies\\)\u00a0 x – 4 = 0\u00a0 \u00a0or\u00a0 \u00a02x – 4 = 0<\/p>\n

\\(\\implies\\)\u00a0 x = 4\u00a0 \u00a0or\u00a0 \u00a0x\u00a0 = \\(3\\over 2\\)<\/p>\n

Hence, x = 4 and x = \\(3\\over 2\\)\u00a0 are the roots of the given equation.<\/p>\n

Example<\/strong><\/span> : Solve the equation : \\(3x^2 – 14x – 5\\) = 0.<\/p>\n

Solution<\/span><\/strong> : We have, \\(3x^2 – 14x – 5\\) = 0<\/p>\n

\\(3x^2 – 15x + x – 5\\) = 0<\/p>\n

3x (x – 5) + 1 (x – 5) = 0<\/p>\n

(x – 5) (3x + 1) = 0<\/p>\n

\\(\\implies\\)\u00a0 x – 5 = 0\u00a0 \u00a0or\u00a0 \u00a03x + 1 = 0<\/p>\n

\\(\\implies\\)\u00a0 x = 5\u00a0 \u00a0or\u00a0 \u00a0x\u00a0 = -\\(1\\over 3\\)<\/p>\n

Hence, x = 5 and x = -\\(1\\over 3\\)\u00a0 are the roots of the given equation.<\/p>\n\n\n

\n
Next – Solve Quadratic Equation by Completing the Square<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Solution of Quadratic Equation of Class 10<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn how to solve quadratic equation by factorisation with examples. Let’s begin – Solve Quadratic Equation by Factorisation Step 1. Splitting of middle term : (i) If the product of a and c = +ac then we have to choose two factors ac whose sum is equal to b. (ii) If the …<\/p>\n

Solve Quadratic Equation by Factorisation<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[42],"tags":[560,567],"yoast_head":"\nSolve Quadratic Equation by Factorisation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn how to solve quadratic equation by factorisation with examples.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/solve-quadratic-equation-by-factorisation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Solve Quadratic Equation by Factorisation - 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