For how many integer values of a does the equation x^2 + ax + 6a = 0 have integer solutions for x?
+421 Firstly, we factor this equation as a(x+6)=−x2. Because −x2≠(−x)2, we have a(x+6)=−1(x2), so a(−x−6)=x2.
There are 18 integer solutions. Only 1 is positive for a, and two are non negative.
