Question

3 of 10
what are the zeros to the function?
f(x) = x² - 49
*type the numbers separated by a comma. no spaces.
enter answer here

Explanation:

Step1: Set the function to zero

To find the zeros of the function \( f(x) = x^2 - 49 \), we set \( f(x) = 0 \), so we have the equation \( x^2 - 49 = 0 \).

Step2: Solve the quadratic equation

We can rewrite the equation as a difference of squares: \( x^2 - 7^2 = 0 \). Using the difference of squares formula \( a^2 - b^2=(a - b)(a + b) \), we factor the left - hand side: \( (x - 7)(x + 7)=0 \).

According to the zero - product property, if \( ab = 0 \), then either \( a = 0 \) or \( b = 0 \). So we set each factor equal to zero:

• If \( x - 7=0 \), then \( x = 7 \).
• If \( x + 7=0 \), then \( x=-7 \).

Answer:

-7,7