Let be a quadratic polynomial with complex coefficients whose coefficient is 1. Suppose the equation has four distinct solutions,

Let $P(x)$ be a quadratic polynomial with complex coefficients whose $x^2$ coefficient is 1. Suppose the equation $P(P(x))=0$ has four distinct solutions, $x=3,4,a,b$. Find the sum of all possible values of $(a+b)^2$.