Question

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

Options

• rational and equal

• irrational and unequal

• irrational and equal

• rational and unequal

Answer 1

Rational and Unequal

Explanation:

 For ax² + bx + c = 0 the roots are `(-b ± sqrt(b^2 - 4ac))/(2a)`. If a, b, c are rational and the discriminant D = b² – 4ac is positive and a perfect square, then `sqrt(D)` is rational, so both roots are rational; D > 0 makes them distinct (unequal).