  Consider the $n$th degree polynomial equation,
$X^n+A_{n-1}X^{n-1}+...+A_1X+A_0=0$ over the ring of 2 by 2 complex matrices.
If this equation has more than ${2n \choose 2}$ solutions, then it has
infinitely many solutions. We show here that for any $n,m \in\N$ such that
$m\leq{2n \choose 2}$, there exists an $n$th degree polynomial equation with
exactly $m$ solutions.
