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B.Math 2008 , polynomial

Source: 10+2

April 16, 2012
algebrapolynomialalgebra proposed

Problem Statement

Suppose that P(x)P(x) is a polynomial with real coefficients, such that for some positive real numbers cc and dd, and for all natural numbers nn, we have c∣n∣3≤∣P(n)∣≤d∣n∣3c|n|^3\leq |P(n)|\leq d|n|^3.
Prove that P(x)P(x) has a real zero.
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