Answer

The discriminant b² - 4ac of a quadratic equation.

ax² + bx + c = 0 gives the clear idea about the nature of the roots of the quadratic equation.

If the discriminant D = b² - 4ac > 0 the quadratic equation has distinct and roots.

If b² - 4ac = 0, the quadratic equation has roots.

If b² - 4ac < 0 has no real roots.

By the value of the discriminant, we can state the nature of the roots of a quadratic equation without actually finding them.