2024 Mock AMC 12 - Problem 11

The polynomial expression x^4 - 14x^3 + ax^2 - bx + 36 has exactly two positive integer roots of multiplicity 2, for a, b \in \mathbb{R}. What is a + b?

\textbf{(A) }132\qquad\textbf{(B) }145\qquad\textbf{(C) }168\qquad\textbf{(D) }185\qquad\textbf{(E) }200