2020 AIME I Problem 14

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.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.