For how many integer values of a does the equation x^2 + ax + 18a = 0 have integer solutions for x?
x^2 + ax + 18a = 0
For integer solutions, the discriminant must = 0 ( or evaluate to a perfect square)
a^2 - 4 (1)(18a) = 0
a^2 - 72a = 0
a ( a - 72) = 0
a = 0 or a = 72 will give us integer solutions