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Polynomial Roots

Problem

Let $P(x) = x^n + c_{n-1}x^{n-1} + ... + c_{2}x^2 + c_{1}x + c_0$, where each of the coefficients, $c_{k}$, are integer. Prove that the roots of the equation $P(x) = 0$ will either be irrational or integer.

Problem ID: 373 (07 Aug 2010)     Difficulty: 3 Star

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