Find the zeros of the quadratic function by factoring. What are the -intercepts of the graph of the function?
:
Select the correct choice below and fill in the answer box to complete your choice.
(Use comma to separate answers as needed. Type an integer or a simplfied fraction.)
A. The zeros and the -intercepts are different. The zeros are
B. The zeros and the -intercepts are the same. They are

Ask by Nguyen Ellis. in the United States

Mar 15,2025

Question

Find the zeros of the quadratic function by factoring. What are the -intercepts of the graph of the function?
:
Select the correct choice below and fill in the answer box to complete your choice.
(Use comma to separate answers as needed. Type an integer or a simplfied fraction.)
A. The zeros and the -intercepts are different. The zeros are
B. The zeros and the -intercepts are the same. They are

Ask by Nguyen Ellis. in the United States

Mar 15,2025

UpStudy AI · Accepted Answer

We start with the function:  
$$
P(x)=3x^2-75
$$

To find the zeros, we set $$ P(x) = 0 $$:
$$
3x^2 - 75 = 0
$$

First, divide both sides by 3:
$$
x^2 - 25 = 0
$$

Recognize that $$ x^2 - 25 $$ is a difference of squares:
$$
x^2 - 25 = (x - 5)(x + 5)
$$

Set each factor equal to zero:
$$
x - 5 = 0 \quad \text{or} \quad x + 5 = 0
$$

Thus:
$$
x = 5 \quad \text{or} \quad x = -5
$$

Since the zeros and the $$ x $$-intercepts of a function are the same, the correct choice is:

B. The zeros and the $$ x $$-intercepts are the same. They are $$ 5, -5 $$.
The zeros and $$ x $$-intercepts are the same. They are 5 and -5.