AMC 12 2012b Problem 13

Two parabolas have equations $y= x^2 + ax +b$ and $y= x^2 + cx +d$, where $a$, $b$, $c$, and $d$ are integers, each chosen independently by rolling a fair six-sided die. What is the probability that the parabolas will have at least one point in common?

\textbf{(A)}\ \frac{1}{2} \textbf{(B)}\ \frac{25}{36} \textbf{(C)}\ \frac{5}{6} \textbf{(D)}\ \frac{31}{36} \textbf{(E)}\ 1