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

1. real and equal

2. real, distinct and rational

3. real, distinct and irrational

4. no real roots

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.

Hence, option 3 is the correct option.