Question

The values of k for which the quadratic equation, 9x² – 3kx + k = 0, has equal roots, are:

Options

• 0, 1

• 0, 2

• 2, 4

• 0, 4

Answer 1

0, 4

Explanation:

Comparing 9x² – 3kx + k = 0 with ax² + bx + c = 0 we get,

a = 9, b = –3k and c = k.

We know that,

Since equations has equal roots,

⇒ D = 0

⇒ b² – 4ac = 0

⇒ (–3k)² – 4(9)(k) = 0

⇒ 9k² – 36k = 0

⇒ 9k(k – 4) = 0

⇒ 9k = 0 or (k – 4) = 0   ...[Using zero-product rule]

⇒ k = 0 or k = 4.