Try using the Intermediate Value Theorem. Does that give you any ideas?
It seems like I'm not doing anything though f(0) = -1 and f(1) = 1 and all you say is therefore by the intermediate value there must exist an x such that f(x) = 0 because f(0) is negative and f(1) is positive?
Am I missing any steps in the proof? Just lean on the theorem and do nothing?