Unlikely Intersection For Two-Parameter Families of Polynomials

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}$$suchthateach$c_i$ is preperiodic for the action of the polynomial $x^d+ax+b$ is not Zariski dense in the affine plane.