Question

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal, then the value of k is ______.

Options

• 2

• 8

• 4

• none of these

Answer 1

If the roots of the quadratic equation 2x² + 8x + k = 0 are equal, then the value of k is 8.

Explanation:

Comparing 2x² + 8x + k = 0 with ax² + bx + c = 0 we get,

a = 2, b = 8 and c = k.

We know that,

Since equations has equal roots,

⇒ Discriminant = 0

⇒ b² – 4ac = 0

⇒ (8)² – 4(2)(k) = 0

⇒ 64 – 8k = 0

⇒ 8k = 64

⇒ k = `64/8`

⇒ k = 8