. Quadratic Equations Introduction Arab mathematician Abraham bar Hiyya Ha-Nasi, often known by the Latin name Savasorda, is famed for his book ‘Liber Embadorum’ published in AD(CE) which is the first book published in Europe to give the complete solution of a quadratic equation. For a period of more than three thousand years beginning from early civilizations to current times, humanity knew how to solve a general quadratic equation in terms of its co-efficients by using four arithmetical operations and extraction of roots. This process is called “Solving by Radicals”.
Huge amount of research has been carried to this day in solving various types of equations. Quadratic Expression An expression of degree n in variable x is a x a x a x ... where a ¹ and a a a n ,... are real numbers.
a a n , ... are called coefficients of the expression. In particular an expression of degree is called a Quadratic Expression which is expressed as p x ax bx a ¹ and a, b, c are real numbers. .
. Zeroes of a Quadratic Polynomial Let p ( x ) be a polynomial. x=a is called zero of p ( x ) if p ( a )= For example, if p ( x )= x – x– then p (– )= + – = and p ( )= – – = Therefore, – and are zeros of the polynomial p ( x )= x – x– . Algebra .
. Roots of Quadratic Equations Let ax bx ≠ , ( ) be a quadratic equation. The values of x such that the expression ax bx + + becomes zero are called roots of the quadratic equation ax bx We have, ax bx + = a x a x + = a x + = since a ≠