In polynomials you have seen expressions of the form x² + 3x - 4. Also we know that when an expression is equated to zero or some other expression, we call it an equation. The equations of the second degree in a single variable "x" or "y" are generally referred to as quadratic equations and the most general form of it is

ax² + bx + c = 0. The roots or solution for the quadratic equation can be obtained by substituting different values for x and selecting that value for which the value of the equation is zero. The methods which we have seen in factorization of polynomials are also applicable to obtain the roots of a quadratic equation. However, in this part we look at a specific method which is only applicable to solve quadratic equations.

According to this method the roots of a quadratic equation ax² + bx + c = 0 are

x

=

and x

=

This is derived as follows. We have

         ax² + bx + c       = 0

         ax² + bx             = - c                                         ........(1)

On dividing equation (1) by a, we have x2 +

In order to make the LHS a perfect square, we add to     to the LHS and since the equality is to be preserved we do so for the other side also. Hence we obtain

x2 +