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For how many integer values of a does the equation \(x^2 + ax + 5a = 0\) have integer solutions for x?

 Dec 20, 2018
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To   have integer solutions.....the discriminant must  either possibly  = 0   or possibly be a  perfect square.....so

 

a^2 - 4(5a) = 0

 

a^2 - 20a  =  0

 

a ( a - 20) = 0

 

Setting each factor to 0 and solving for a   produces  a =  0   or  a = 20

 

Or

 

a^2 - 20a   = perfect square

 

a (a - 20)  = perfect square

 

This happens when   a = 20  , a = 0 , a = -16  or a  =  36

 

So....4 values for a  produce integer solutions

 

 

cool cool cool

 Dec 20, 2018

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