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For how many integer values of a does the equation x^2 + ax + 6a = 0 have inetger solutions for x?

Oct 12, 2020

The discriminant must be a perfect square: $$a^2-24a=k^2\rightarrow a(a-24)=k^2$$. From here it is casework: https://www.wolframalpha.com/input/?i=solve+a%28a-24%29%3Dk%5E2+over+the+integers