Question

find the zeros of the quadratic by factoring and using the zero product property.
$x^2 + 5x - 24 = 0$
a. $x = -5$ and $x = 24$
b. $x = -8$ and $x = 3$
c. $x = -3$ and $x = 8$
d. $x = 6$ and $x = -4$

Explanation:

Step1: Factor the quadratic

We need two numbers that multiply to $-24$ and add to $5$. These numbers are $8$ and $-3$.
$x^2 + 5x - 24 = (x + 8)(x - 3) = 0$

Step2: Apply zero product property

Set each factor equal to 0:
$x + 8 = 0$ or $x - 3 = 0$

Step3: Solve for x

For $x + 8 = 0$: $x = -8$
For $x - 3 = 0$: $x = 3$

Answer:

b. x = -8 and x = 3