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QUADRATIC EQUATIONS:

HISTORY OF QUADRATIC EQUATIONS

The word quadratic is derived from the Latin word “Quadratum” which means “A square figure”. Brahmagupta (an ancient Indian Mathematician)(A.D. 598-665) gave an explicit formula to solve a quadratic equation. Later Sridharacharya (A.D. 1025) derived a formula, now known as the quadratic formula, for solving a quadratic equation by the method of completing the square. An Arab mathematician Al-khwarizni(about A.D. 800) also studied quadratic equations of different types. It is believed that Babylonians were the first to solve quadratic equations. Greek mathematician Euclid developed a geometrical approach for finding lengths, which are nothing but solutions of quadratic equations.

INTRODUCTION

A polynomial of degree two is called a quadratic polynomial. When a quadratic polynomial is equated to zero, it is called a quadratic equation. A quadratic equation of the form ax^2 bx + c = 0, a > 0, where a, b, c are constants and x is a variable is called a quadratic equation in the standard form.

Roots Of Quadratic Equation

A zero of a polynomial is that real number, which when substituted for the variable makes the value of the polynomial zero. In case of a quadratic equation, the value of the variable for which LHS and RHS of the equation become equal is called a root or solution of the quadratic equation. There are three algebraic methods for finding the solution of a quadratic equation. These are

(i) Factor Method

(ii) Completing the square method and

(iii) Using the Quadratic Formula.

FACTORIZATION METHOD

Factorisation method is used when the quadratic equation can be factorised into two linear factors. After factorisation, the quadratic equation is expressed as the product of its two linear factors and this is equated to zero.