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.