Prove that there is no complex root such that both the Re and Im parts are rational.

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.

Like in

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