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Show that $P(X)$ is a first degree polynomial.

Source: Moldova TST 1999

August 7, 2023
algebrapolynomial

Problem Statement

Let P(X)P(X) be a nonconstant polynomial with real coefficients such that for every rational number qq{} the equation P(X)=qP(X)=q has no irrational solutions. Show that P(X)P(X) is a first degree polynomial.
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