Question

use factoring to find the real zeros of the function.
g(x)=x² - 121
select the correct choice and, if necessary, fill in the answer box to complete your choice.
○ a. the real zero(s) of the function is/are x =
(type an integer or a simplified fraction. use a comma to separate answers as needed.)
○ b. there are no real zeros.

Explanation:

Step1: Recognize difference of squares

The function \( g(x) = x^2 - 121 \) is a difference of squares, since \( x^2 = (x)^2 \) and \( 121 = 11^2 \). The formula for factoring a difference of squares is \( a^2 - b^2 = (a - b)(a + b) \).
So, \( g(x) = (x - 11)(x + 11) \).

Step2: Find real zeros

To find the real zeros, set \( g(x) = 0 \):
\( (x - 11)(x + 11) = 0 \)
Using the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \).
So, \( x - 11 = 0 \) or \( x + 11 = 0 \).
Solving \( x - 11 = 0 \) gives \( x = 11 \).
Solving \( x + 11 = 0 \) gives \( x = - 11 \).

Answer:

A. The real zero(s) of the function is/are \( x = - 11,11 \)