  Let $c_1, c_2, c_3$ be distinct complex numbers, and let $d\ge 3$ be an
integer. We show that the set of all pairs $(a,b)\in \mathbb{C}\times
\mathbb{C}$ such that each $c_i$ is preperiodic for the action of the
polynomial $x^d+ax+b$ is not Zariski dense in the affine plane.

Dynamical Systems;Algebraic Geometry;Number Theory