Find the value of k for which the roots of the following equation are real and equal. k 2 x 2 - 2(2k - 1)x + 4 = 0

Given, Equation : k 2 x 2 - 2(2k - 1)x + 4 = 0 The roots of the equation are real and equal, when D = 0. ⇒ b 2 - 4ac = 0 ⇒ [-2(2k - 1)] 2 - 4 × k 2 × 4 = 0 ⇒ [-4k + 2] 2 - 16k 2 = 0 ⇒ 16k 2 + 4 - 16k - 16k 2 = 0 ⇒ 16k = 4 ⇒ k = . Hence, k = .