What are the zeros of the function f(x)=x^2−5x−24

8 and -3

Start by factoring the equation:

(x + 3)(x - 8)

Then set each equal to zero and solve for each one. 

We need to put this in factored form. I can explain factored form if you want, but for now I’ll just show you the result.
(X-8)(x+3)
We can check if this is the right equation.
X^2 +3x-8x-24
So, we have the factored form and it will be very easy to find the zeros.
(X-8)(x+3)
We need for that to equal zero. Whenever you multiply anything by y zero, you’ll receive zero.
X=8, x=-3
They will satisfy the equation and will get you zero. Let’s check.
8^2-5(8)-24
64-40-24
24-24
0
So 8 works.
-3^2-5(-3)-24
9+15-24
24-24
0
So, the zeros are 8 and -3.