I have this quadratic:
-2x^2-19x-24
I need to find its zeros and factor it but I havent had any luck. I also tried the quadratic formula but it produces negative roots? any help is welcomed
$\displaystyle -2x^2 - 19x - 24 = 0$.
Do you know about the discriminant?
$\displaystyle \Delta = b^2 - 4ac$.
If the discriminant is positive, we have two solutions, if it is 0 we have one solution, and if it is negative we don't have any solutions.
$\displaystyle \Delta = (-19)^2 - 4(-2)(-24)$
$\displaystyle = 361 - 192$
$\displaystyle = 169$.
Since this is positive, there are two solutions.
The solutions are given by
$\displaystyle x = \frac{-b \pm \sqrt{\Delta}}{2a}$
$\displaystyle = \frac{19 \pm \sqrt{169}}{2(-2)}$
$\displaystyle = \frac{19 \pm 13}{-4}$
$\displaystyle = \frac{6}{-4}$ or $\displaystyle = \frac{32}{-4}$
$\displaystyle = -\frac{3}{2}$ or $\displaystyle = -8$.