Question 64
Let $a$, $b$, $c$ be integers. Define $f(x) = a x^{2} + b x + c$. Suppose there exist pairwise distinct integers $u$, $v$, $w$ such that $f(u) = 0$, $f(v) = 0$, and $f(w) = 2$. Find the maximum possible value of the discriminant $b^{2} - 4 a c$ of $f$.