Let be a polynomial with integer (real) coefficients such that; (1) - the coefficient of the leading term and the coefficient of the independent term (counted as the coefficient of degree) are odd; (2) -The total number of odd coefficients is odd.

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Prove that has no root such that both the real and the imaginary parts are rational. In other words, if is a root of , then at least one of the numbers and is irrational