I have one doubt.
Suppose, $f_{n}(x)=a_0x^n+a_1x^{n-1}+a_2x^{n-2}+,...,+a_{n-1}x+a_n=0$ be a polynomial with an integral coefficients. If for some $n$ ( say $n=2 \ or \ 3$) , $f_{n}(t)=0,$ where, $t \notin \mathbb{Z}$.
Can I say that all the roots of the polynomial $f_{n}(x)$ are not an integral roots.
Here I want to prove that the polynomial is not an integral,(here $f_n(1) \ \& f_n(0)$ are not odd)