CMO 1971

$ABCD$ is a quadrilateral with $AD=BC$ . If $\angle ADC$ is greater than $\angle BCD$ , prove that $AC>BD$ .

Let $$p(x) = a_nx^n + a_{n-1}x^{n-1} + \cdots + a_1x+a_0,$$ where the coefficients $a_i$ are integers. If $p(0)$ and $p(1)$ are both odd, show that $p(x)$ has no integral roots.