{"id":6669,"date":"2021-10-19T15:34:22","date_gmt":"2021-10-19T10:04:22","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6669"},"modified":"2021-11-27T23:34:10","modified_gmt":"2021-11-27T18:04:10","slug":"what-is-quadratic-equation-in-standard-form","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-quadratic-equation-in-standard-form\/","title":{"rendered":"What is Quadratic Equation in Standard Form"},"content":{"rendered":"

Here you will learn quadratic equation concepts and what is quadratic equation in standard form.<\/p>\n

Let’s begin – <\/p>\n

Quadratic Equation<\/h2>\n

If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation.<\/p>\n

For example, \\(x^2 + 2x – 8\\) = 0, \\(x^2 – 5x + 6\\) = 0 are quadratic equations.<\/p>\n

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

What is Quadratic Equation in Standard Form ?<\/h2>\n

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

For example, \\(5x^2 + 3x + 6\\) = 0 is a quadratic equation in the standard form.<\/p>\n

Rule to Determine Whether Equation is Quadratic or Not<\/h2>\n

1). Write down the given equation in the form f(x) = 0.<\/p>\n

2). (a) If f(x) is a polynomial, then observe its degree.<\/p>\n

(b) If f(x) is not a polynomial, then first make it poynomial and then observe its degree.<\/p>\n

3). If degree of the polynomial is 2, then the given equation is quadratic.<\/p>\n

Example<\/strong><\/span> : Which of the following are quadratic equation ?<\/p>\n

(i) \\(x^2 -6x – 4\\) = 0<\/p>\n

(ii) x + 2 = 0<\/p>\n

(iii) x + \\(1\\over x\\) = 1,  x \\(\\ne\\) 0<\/p>\n

(iv) \\(x^2\\) + \\(1\\over x\\) = 1,  x \\(\\ne\\) 0<\/p>\n

Solution<\/span><\/strong> : <\/p>\n

(i) p(x) = \\(x^2 -6x – 4\\) is polynomial with degree 2.<\/p>\n

\\(\\therefore\\)  \\(x^2 -6x – 4\\) = 0 is a quadratic equation.<\/p>\n

(ii) p(x) = x + 2 is polynomial with degree 1.<\/p>\n

\\(\\therefore\\)  x + 2 = 0 is not a quadratic equation.<\/p>\n

(iii) x + \\(1\\over x\\) = 1 \\(\\implies\\) \\(x^2 + 1\\over x\\) = 1 \\(\\implies\\) \\(x^2 +1\\) = x \\(\\implies\\) \\(x^2 – x + 1\\) = 0<\/p>\n

Since, here p(x) = \\(x^2 – x + 1\\) is polynomial with degree 2.<\/p>\n

\\(\\therefore\\)  \\(x^2 – x + 1\\) = 0 is a quadratic equation.<\/p>\n

(iv)  \\(x^2\\) + \\(1\\over x\\) = 1 \\(\\implies\\) \\(x^3 + 1\\over x\\) = 1 \\(\\implies\\) \\(x^3 +1\\) = x \\(\\implies\\) \\(x^3 – x + 1\\) = 0<\/p>\n

Here, p(x) = \\(x^3 – x + 1\\) is polynomial with degree 3.<\/p>\n

\\(\\therefore\\)  \\(x^3 – x + 1\\) = 0 is not a quadratic equation.<\/p>\n\n\n

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

Here you will learn quadratic equation concepts and what is quadratic equation in standard form. Let’s begin –  Quadratic Equation If p(x) is a quadratic polynomial, then p(x) = 0 is called a quadratic equation. For example, \\(x^2 + 2x – 8\\) = 0, \\(x^2 – 5x + 6\\) = 0 are quadratic equations. The …<\/p>\n

What is Quadratic Equation in Standard Form<\/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":[560,570],"yoast_head":"\nWhat is Quadratic Equation in Standard Form - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn quadratic equation concepts and what is quadratic equation in standard form.\" \/>\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\/what-is-quadratic-equation-in-standard-form\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is Quadratic Equation in Standard Form - 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