Question

The value of k for which the equation x² + 2(k + 1)x + k² = 0 has equal roots is:

Options

• –1

• `-1/2`

• 1

• none of these

Answer 1

`-1/2`

Explanation:

For equal roots, D = 0

⇒ [2(k + 1)]² – 4 × k² = 0

⇒ 4(k + 1)² – 4k² = 0

⇒ 4(k² + 2k + 1) – 4k² = 0

⇒ 8k + 4 = 0

⇒ k = `−1/2`