Determine all values of k so that the trinonmial can be factored using integers
$\displaystyle c^2+kc-24$
I think it might be 10 and 2 but im really not so sure. :/
Help please
Do you know the discriminant ? If yes, then you know that if the discriminant is a perfect square, the quadratic can be factored over the integers. Here the discriminant is equal to :
$\displaystyle \Delta = k^2 + 96$
So, it means that for some $\displaystyle a^2$, the following holds :
$\displaystyle a^2 = k^2 + 96$
Or, rearranging :
$\displaystyle a^2 - k^2 = 96$
Finally :
$\displaystyle (a - k)(a + k) = 96$
Now you can factorize $\displaystyle 96$ and see which values of $\displaystyle k$ actually satisfy this equation. I'm pretty sure you are right with 2 and 10.