Question

If the discriminant of a quadratic equation, ax² + bx + c = 0, is greater than zero and a perfect square and b is irrational, then the roots are:

Options

• irrational and unequal

• irrational and equal

• rational and unequal

• rational and equal

Answer 1

Irrational and Unequal

Explanation:

The roots are `x = (-b ± sqrt(D))/(2a)` with D = b² – 4ac. Here D > 0 so the two roots are distinct. Since D is a perfect square, `sqrt(D)` is rational, but b is given irrational, hence `(-b ± sqrt(D))` is irrational and dividing by 2a (nonzero) keeps them irrational. Therefore, the two roots are irrational and unequal.