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Q. Prove that a polynomial $f(x)$,with integer coefficients has no integral roots if $f(0)$ and $f(1)$ are both odd integers.
now $f(0)=a_0$ which is an odd integer. and $f(1)=(a_0+a_1+a_2+\dots+a_n$) an odd integer.
Now, what is the strategy I need to imply to prove that $f(x)$ can't have integral roots.