For this question, f(x) = 4kx² + (4k + 2)x + 1, where k is a real constant.

a. Find the discriminant of f(x) in terms of k.

b. By simplifying your answer to part a or otherwise, prove that f(x) has two distinct real roots for all non-zero values of k.

c. Explain why f(x) cannot have two distinct real roots when k = 0.