The given quadratic equation is (3k + 1)x2 + 2(k + 1)x + 1 = 0. Since the given quadratic equation has equal roots, its discriminant should be zero.
D = 0 ⇒ 4(k + 1)2 − 4 × (3k + 1) × 1 = 0
⇒ 4k2 + 8k + 4 − 12k − 4 = 0
⇒ 4k2 − 4k = 0
⇒ 4k(k−1) = 0
⇒ k = 0 or 1
Thus, the values of k are 0 and 1.