Question

The nature of roots of quadratic equation 3x² − 6x − 3 = 0 are ______.

Options

• real and equal

• real, distinct and rational

• real, distinct and irrational

• no real roots

Answer 1

The nature of roots of quadratic equation 3x² − 6x − 3 = 0 are real, distinct and irrational.

Explanation:

Comparing 3x² − 6x − 3 = 0 with ax² + bx + c = 0, we get:

a = 3, b = −6, c = −3

We know that,

⇒ D = b² − 4ac

⇒ D = (−6)² − 4 × (3) × (−3)

⇒ D = 36 + 36

⇒ D = 72

∴ D > 0 and not a perfect square. Roots are real, distinct and irrational.