Question

The roots of a quadratic equation are irrational. Then

• A. discriminant \(> 0 \)
• B. discriminant \(<0\)
• C. discriminant is a perfect square
• D. discriminant is not a perfect square

Answer 1

The Correct Option is D

For a quadratic equation \( ax^2 + bx + c = 0 \), the nature of its roots is determined by the discriminant \( D = b^2 - 4ac \). The roots are:
Real and rational if \( D > 0 \) and \( D \) is a perfect square.
Real and irrational if \( D > 0 \) and \( D \) is not a perfect square.
Complex (imaginary) if \( D < 0 \).

Since the roots are given to be irrational, this means: \( D > 0 \) and \( D \) is not a perfect square.

Hence, the correct answer is that the discriminant is not a perfect square.