I'm stuck on this problem. Let a and b be fixed non-zero real numbers and let f(x) = 2(b^2)x^3 + abx^2 - [(a^2) + (3b^2) + 1] - 3ab. Prove that f(x) = 0 has three real roots and one of these roots must lie in the interval [-1,1]. Thank you for your help.