Let f (x) be a monic polynomial of odd degree. Prove that for some A < 0,

f (A) < −1 and for some B > 0, f (B) > 1. Deduce that every polynomial of odd degree has a real root.

Suppose f(x) =x^(2n+1)+a2n x^(2n)...+a1x+a0, but I've no clue how to go from here. Could anyone please give me some hints? Any help is appreciated!