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For how many integer values of a does the equation x^2 + ax + 18a = 0 have integer solutions for x?

 Dec 22, 2020
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x^2  + ax  + 18a  =  0

 

For integer solutions, the discriminant  must   = 0    (  or evaluate to a perfect square)

 

So....

 

a^2 - 4 (1)(18a)   = 0

 

a^2  - 72a  =  0

 

a ( a - 72)   =  0

 

a  =  0      or       a =  72      will   give us integer solutions 

 

 

cool cool cool

 Dec 22, 2020

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