Find the values of k for which the following equation has equal roots:

3kx² = 4(kx - 1)

⇒ 3kx² = 4(kx - 1)

⇒ 3kx² = 4kx - 4

⇒ 3kx² - 4kx + 4 = 0

Comparing 3kx² - 4kx + 4 = 0 with ax² + bx + c = 0 we get,

a = 3k, b = -4k and c = 4.

Since equations has equal roots,

∴ D = 0

⇒ (-4k)² - 4 × (3k) × 4 = 0

⇒ 16k² - 48k = 0

⇒ 16k(k - 3) = 0

⇒ 16k = 0 or (k - 3) = 0      [Using Zero-product rule]

⇒ k = 0 or k = 3

Hence, k = {0, 3}.