If the quadratic equation kx² + kx + 1 = 0 has real and distinct roots, the value of k is :

1. 0

2. 4

3. 0 and 4

4. 0 or 4

Comparing equation kx² + kx + 1 = 0, with ax² + bx + c = 0 , we get :

a = k, b = k and c = 1.

Since, quadratic equation has real and distinct roots.

∴ D > 0

∴ b² - 4ac > 0

⇒ k² - 4 × k × 1 > 0

⇒ k² - 4k > 0

⇒ k(k - 4) > 0

⇒ k > 0 or k > 4.

Considering k > 0,

k = 4 can give real and distinct roots for kx² + kx + 1 = 0.

Hence, Option 2 is the correct option.