Question 58
Given the polynomial $p(x) = x(x+1)(x-2)^2$, consider the polynomial $q(x) = p(p(p(\ldots(p(x)) \ldots)))$ obtained by composing $p(x)$ with itself 2024 times. How many integers $k$ are there such that $q(k) = 0$?
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6
(A) 1
(B) 3
(C) 4
(D) 5
(E) 6