Question

the zeros of the function $p(x) = x^2 - 2x - 24$ are

a. $-8$ and $3$

b. $-6$ and $4$

c. $-4$ and $6$

d. $-3$ and $8$

Explanation:

Step1: Factor the quadratic function

To find the zeros of \( p(x) = x^2 - 2x - 24 \), we factor the quadratic. We need two numbers that multiply to \(-24\) and add to \(-2\). The numbers are \(-6\) and \(4\) (since \(-6 \times 4 = -24\) and \(-6 + 4 = -2\)). So, \( p(x) = (x - 6)(x + 4) \).

Step2: Find the zeros

Set each factor equal to zero:

• \( x - 6 = 0 \) gives \( x = 6 \)
• \( x + 4 = 0 \) gives \( x = -4 \)

Answer:

c. \( -4 \) and \( 6 \)