For how many integer values of 'a' does the equation
x^2 + ax + 8 = 0
have integer solutions for x?
It isn't 4.
Sorry, I meant x^2 + ax + 8a = 0.
Hint: use the quadratic formula as \(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)and $a=1$, $b=a$ and $c=8$
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
Sorry, that's incorrect. The correct answer was 8.
