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

x² - 2kx + 7k - 12 = 0

Comparing x² - 2kx + 7k - 12 = 0 with ax² + bx + c = 0 we get,

a = 1, b = -2k and c = (7k - 12).

Since equations has equal roots,

∴ D = 0

⇒ (-2k)² - 4 × 1 × (7k - 12) = 0

⇒ 4k² - (28k - 48) = 0

⇒ 4k² - 28k + 48 = 0

⇒ 4k² - 16k - 12k + 48 = 0

⇒ 4k(k - 4) - 12(k - 4) = 0

⇒ (k - 4)(4k - 12) = 0

⇒ (k - 4) = 0 or (4k - 12) = 0      [Using Zero-product rule]

⇒ k = 4 or 4k = 12

⇒ k = 4 or k = $\dfrac{12}{4}$

⇒ k = 4 or k = 3.

Hence, k = {4, 3}.