QUADRATIC EQUATIONS

NATURE OF ROOTS OF A QUADRATIC EQUATION

• Roots of the general quadratic equation were obtained as,

This indicates that in general a quadratic equation has two roots. But the nature of these roots depends on the value of

• If is positive its square root is a real non zero number and the equation will have two real and unequal roots. In this case we say that the roots of the quadratic equation are real and distinct.

• If is zero we get only one solution,

For the equation and we say that the equation has two coincident (or repeated) roots.

If is negative it has no real square roots and we say that the roots of the equation are not real.

• So we have,

• The converse of these are true.

• The expression is called the discriminant of the equation and is denoted by .

• From the above conditions we also have,