Barrett Guerrero
07/02/2023 · Primary School

What are the zeros of \( f(x)=(x-2)(x+7) \) ? Select all that apply. \( \square \) A. \( x=7 \) \( \square \) B. \( x=-2 \) \( \square \) C. \( x=2 \) \( \square \) D. \( x=-7 \)

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To find the zeros of the function \( f(x) = (x-2)(x+7) \), we need to set the function equal to zero and solve for \( x \): \[ f(x) = 0 \implies (x-2)(x+7) = 0 \] This equation is satisfied when either factor is equal to zero: 1. \( x - 2 = 0 \) gives \( x = 2 \) 2. \( x + 7 = 0 \) gives \( x = -7 \) Thus, the zeros of the function \( f(x) \) are \( x = 2 \) and \( x = -7 \). Now, let's check the options: - \( A. \, x = 7 \) (not a zero) - \( B. \, x = -2 \) (not a zero) - \( C. \, x = 2 \) (is a zero) - \( D. \, x = -7 \) (is a zero) The correct answers are: - \( \square \) A. \( x=7 \) (not selected) - \( \square \) B. \( x=-2 \) (not selected) - \( \square \) C. \( x=2 \) (selected) - \( \square \) D. \( x=-7 \) (selected) So, the selected options are C and D.

Quick Answer

The zeros are \( x=2 \) and \( x=-7 \).
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