From NYCIML (F18SA03):
For how many ordered pairs of integers $(a,b)$ with $a,b\in\{1,2,\ldots,15\}$ does the equation $ax^2+bx+a=0$ have rational roots?
Would $(a,b)=(1,2)$ (corresponding to the equation $x^2+2x+1=0$, which has $-1$ as a repeated rational root) be considered a solution? That is, does a repeated root count as "roots" (plural)?
(The official solution doesn't consider.)