AMC 12B 2022 (Problem 4)

For how many values of the constant kk will the polynomial x2+kx+36x^2 + kx + 36 have two distinct integer roots?
(A)  6\text{(A)}\;6(B)  8\text{(B)}\;8(C)  9\text{(C)}\;9(D)  14\text{(D)}\;14(E)  16\text{(E)}\;16