Question

If the equation, ax² + 2x + a = 0 has two real and equal roots, then:

Options

• a = 0, 1

• a = 1, 1

• a = 0, –1

• a = –1, 1

Answer 1

a = –1, 1

Explanation:

Comparing ax² + 2x + a = 0 with ax² + bx + c = 0 we get,

a = a, b = 2 and c = a.

We know that,

Since equations has real and equal roots,

⇒ D = 0

⇒ b² – 4ac = 0

⇒ (2)² – 4(a)(a) = 0

⇒ 4 – 4a² = 0

⇒ 4 = 4a² 

⇒ `a^2 = 4/4`

⇒ a² = 1

⇒ `a = sqrt(1)`

⇒ a = ±1

⇒ a = –1, 1