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For how many integer values of 'a' does the equation

x^2 + ax + 8 = 0

have integer solutions for x?

 

It isn't 4.

 Dec 17, 2020
 #1
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Sorry, I meant x^2 + ax + 8a = 0.

 Dec 17, 2020
 #2
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Hint: use the quadratic formula as \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)and $a=1$, $b=a$ and $c=8$

 Dec 17, 2020
 #3
avatar+117724 
+1

x^2  + ax  + 8a   =  0

 

The discriminant either needs to be a perfect square  or  = 0

 

a^2  - 4(8a)  =  0

a^2 - 32a  =  0

a( a - 32)  =  0

If a  = 0 or 32  we will have  integer solutions  ( a double root)

 

So.....two  values of a  will produce integer solutions

 

 

cool cool cool

 Dec 17, 2020
 #4
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Sorry, that's incorrect. The correct answer was 8.

 Dec 18, 2020

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