Question 34
Let
$$
p(x) = a_{0} x^{n} + a_{1} x^{n-1} + \cdots + a_{n-1} x + a_{n}
$$
where the coefficients $a_{i}$ are integers. If $p(0)$ and $p(1)$ are both odd, show that $p(x)$ has no integral roots.
$$
p(x) = a_{0} x^{n} + a_{1} x^{n-1} + \cdots + a_{n-1} x + a_{n}
$$
where the coefficients $a_{i}$ are integers. If $p(0)$ and $p(1)$ are both odd, show that $p(x)$ has no integral roots.