Suppose that $\displaystyle p(x) $ is a polynomial with real coefficients such that for some positive real numbers $\displaystyle c,d $and for all natural numbers $\displaystyle n $ ,we have $\displaystyle c|n|^{3}\leq |p(n)|\leq d|n|^{3} $.

Prove that $\displaystyle p(x) $ has a real zero.

HELP!