{"id":6671,"date":"2021-10-19T16:27:02","date_gmt":"2021-10-19T10:57:02","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6671"},"modified":"2021-11-27T23:33:25","modified_gmt":"2021-11-27T18:03:25","slug":"roots-of-quadratic-equation","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/roots-of-quadratic-equation\/","title":{"rendered":"Roots of Quadratic Equation"},"content":{"rendered":"

Here you will learn what are the roots of quadratic equation with examples.<\/p>\n

Let’s begin – <\/p>\n

Roots of Quadratic Equation<\/h2>\n

If p(x) = 0 is a quadratic equation, then the zeroes of the poynomial p(x) are called the roots of the quadratic equation p(x) = 0.<\/p>\n

Thus, x = 1 is a root of p(x) = \\(x^2 + x – 2\\) = 0<\/p>\n

Since p(1) = \\((1)^2\\) + 1 – 2 = 0<\/p>\n

and, x = -2 is also a root of \\(x^2 + x – 2\\) = 0.<\/p>\n

Since p(-2) = \\((-2)^2\\) + (-2) – 2 = 4 – 2 – 2 = 0.<\/p>\n

Note<\/strong> : <\/p>\n

1). x = \\(\\alpha\\) is a root of p(x) = 0, iff \\(p(\\alpha)\\) = 0.<\/p>\n

2). Every quadratic equation can have atmost two real roots.<\/p>\n

3). Finding the zeroes of the quadratic equations is known as solving the quadratic equation.<\/p>\n

Example<\/strong><\/span> : In each of the following quadratic equations the values of x are given. Determine whether these values are roots of the equations or not.<\/p>\n

(i) \\(2x^2 + 3x + 1\\) = 0;  x = -1<\/p>\n

(ii)  \\(4x^2 – 5x – 6\\) = 0;  x = 2<\/p>\n

Solution<\/span><\/strong> : <\/p>\n

(i)  Putting x = -1, on the left side of the given equation, we get<\/p>\n

L.H.S = \\(2\\times (-1)^2 + 3\\times (-1) + 1\\) = 2 – 3 + 1 = 0 = R.H.S<\/p>\n

So, x = -1 is a root of the given equation.<\/p>\n

(ii)  Putting x = 2, on the left side of the given equation, we get<\/p>\n

L.H.S = \\(4\\times (2)^2 – 5\\times (2) – 6\\) = 16 – 10 – 6 = 0 = R.H.S<\/p>\n

So, x = 2 is a root of the given equation.<\/p>\n\n\n

\n
Next – Solution of Quadratic Equation of Class 10<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – What is Quadratic Equation in Standard Form<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here you will learn what are the roots of quadratic equation with examples. Let’s begin –  Roots of Quadratic Equation If p(x) = 0 is a quadratic equation, then the zeroes of the poynomial p(x) are called the roots of the quadratic equation p(x) = 0. Thus, x = 1 is a root of p(x) …<\/p>\n

Roots 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":[560,569],"yoast_head":"\nRoots of Quadratic Equation - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what are the zeroes or roots of quadratic equation 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\/roots-of-quadratic-equation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Roots of Quadratic Equation - 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