Solve the below:
Q: Assume F has characteristic 0 and K is a splitting field of f (x) in F[x]. If d(x) is the greatest common divisor of f(x) and f ' (x) and h(x) = f(x) / d(x) in F[x], prove that
a) f (x) and h(x) have the same roots in K
b) h (x) is separable