Question

Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is ______.

Options

• 0 only

• 4

• 8 only

• 0, 8

Answer 1

Values of k for which the quadratic equation 2x² – kx + k = 0 has equal roots is 0, 8.

Explanation:

Given equation is 2x² – kx + k = 0

On comparing with ax² + bx + c = 0, we get

a = 2,b = -k and c = k

For equal roots, the discriminant must be zero

i.e., D = b² – 4ac = 0

⇒ (–k)² – 4(2)k = 0

⇒ k² – 8k = 0

⇒ k(k – 8) = 0

∴ k = 0, 8

Hence, the required values of k are 0 and 8.