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

 Oct 24, 2020
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Firstly, we factor this equation as $a(x + 6) = -x^2.$  Because $-x^2 \ne (-x)^2,$ we have $a(x+6)=-1(x^2),$ so $a(-x-6)=x^2.$ 

 

There are 18 integer solutions. Only 1 is positive for a, and two are non negative.

 Oct 24, 2020

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