# Thread: Determine all values of k

1. ## Determine all values of k

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. :/

2. Originally Posted by HAGEMONSTER
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. :/

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.

3. thanks so mu8ch