{"id":6683,"date":"2021-10-19T20:08:40","date_gmt":"2021-10-19T14:38:40","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6683"},"modified":"2021-11-27T23:23:34","modified_gmt":"2021-11-27T17:53:34","slug":"relation-between-roots-and-coefficients-of-quadratic-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/relation-between-roots-and-coefficients-of-quadratic-equation\/","title":{"rendered":"Relation Between Roots and Coefficients of Quadratic Equation"},"content":{"rendered":"

Here you will learn what is the relation between roots and coefficients of quadratic equation with examples.<\/p>\n

Let’s begin –<\/p>\n

The general form of quadratic equation is \\(ax^2 + bx + c\\) = 0,  a \\(\\ne\\) 0.<\/p>\n

The root of the given equation can be found by using the formula :<\/p>\n

\n

x = \\(-b \\pm \\sqrt{b^2 – 4ac}\\over 2a\\)<\/p>\n<\/blockquote>\n

Relation Between Roots and Coefficients of Quadratic Equation<\/h2>\n

(a) Let \\(\\alpha\\) and \\(\\beta\\) be the roots of the quadratic equation \\(ax^2 + bx + c\\) = 0, then<\/p>\n

\n

(i) Sum of roots<\/strong> is \\(\\alpha\\) + \\(\\beta\\) = \\(-b\\over a\\)<\/p>\n

(ii) Product of roots <\/strong>is \\(\\alpha\\) \\(\\beta\\) = \\(c\\over a\\)<\/p>\n

(iii)<\/strong> \\(|\\alpha – \\beta|\\) = \\(\\sqrt{D}\\over | a |\\)<\/p>\n

where D = \\(b^2 – 4ac\\)<\/p>\n<\/blockquote>\n

(b) A quadratic equation whose roots are \\(\\alpha\\) and \\(\\beta\\) is \\((x – \\alpha)\\) \\((x – \\beta)\\) = 0 i.e.<\/p>\n

\n

\\(x^2 – (\\alpha + \\beta)x + \\alpha\\beta\\) = 0<\/p>\n

i.e. \\(x^2\\) – (sum of roots) x + product of roots = 0.<\/p>\n<\/blockquote>\n

Example<\/span><\/strong> : If \\(\\alpha\\) and \\(\\beta\\) are the roots of a quadratic equation \\(x^2 – 3x + 5\\) = 0. Find the sum of roots and product of roots.<\/p>\n

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

Sum of Roots = \\(\\alpha\\) + \\(\\beta\\) = \\(-b\\over a\\) = 3<\/p>\n

Product of Roots = \\(\\alpha\\)\\(\\beta\\) = \\(c\\over a\\) = 5<\/p>\n

Example<\/span><\/strong> : Find the quadratic equation whose sum of roots is 5 and product of roots is 6.<\/p>\n

Solution<\/span><\/strong> : By using the formula,<\/p>\n

\\(x^2\\) – (sum of roots) x + product of roots = 0.<\/p>\n

\\(x^2 – (5)x + (6)\\) =0 \\(\\implies\\) \\(x^2 – 5x + 6\\) = 0<\/p>\n\n\n

\n
Previous – Nature of Roots of Quadratic Equation<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what is the relation between roots and coefficients of quadratic equation with examples. Let’s begin – The general form of quadratic equation is \\(ax^2 + bx + c\\) = 0,  a \\(\\ne\\) 0. The root of the given equation can be found by using the formula : x = \\(-b \\pm \\sqrt{b^2 …<\/p>\n

Relation Between Roots and Coefficients of Quadratic Equation<\/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":[559,560,557,558],"yoast_head":"\nRelation Between Roots and Coefficients of Quadratic Equation<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the relation between roots and coefficients of 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