I have $\displaystyle f(x)=x^n+a_1x^{n-1}+...+a_n$. With integer coefficients.

I know that $\displaystyle f(0)$ and $\displaystyle f(1) $are odd numbers.

I have to prove that $\displaystyle f(x)$ has no roots over $\displaystyle Q$.

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From the fact that $\displaystyle f(0)$ is odd I know that $\displaystyle a_n$ is odd...

Which approach should I use to finish the proof?