Question

If the equation x² – (2 + m)x + (–m² – 4m – 4) = 0 has coincident roots, then:

Options

• m = 0, m = 1

• m = 2, m = 2

• m = –2, m = –2

• m = 6, m = 1

Answer 1

m = –2, m = –2

Explanation:

For coincident roots, D = 0

⇒ [– (2 + m)]² – 4 × 1 × (–m² – 4m – 4) = 0

⇒ (2 + m)² + 4(m² + 4m + 4) = 0

⇒ (2 + m)² + 4(m + 2)² = 0

⇒ 5(2 + m)² = 0

⇒ (2 + m)² = 0

⇒ m = –2