Rogers Bernard
02/14/2023 · Primary School

Suppose that the polynomial function \( f \) is defined as follows. \[ f(x)=(x-11)^{2}(x+4)(x-12)^{2} \] List each zero of \( f \) according to its multiplicity In the categories below. If there is more than one answer for a multiplicty, separate them with commas. If there is no answer, dick on "None." Zero(s) of multiplicity one: Zero(s) of multiplicity two:

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To find the zeros of the polynomial function \( f(x) = (x-11)^{2}(x+4)(x-12)^{2} \), we need to identify the values of \( x \) that make \( f(x) = 0 \) and their corresponding multiplicities. 1. **Finding the zeros:** - The factor \( (x-11)^{2} \) gives a zero at \( x = 11 \) with multiplicity 2. - The factor \( (x+4) \) gives a zero at \( x = -4 \) with multiplicity 1. - The factor \( (x-12)^{2} \) gives a zero at \( x = 12 \) with multiplicity 2. 2. **Listing the zeros according to their multiplicities:** - **Zero(s) of multiplicity one:** - \( -4 \) - **Zero(s) of multiplicity two:** - \( 11, 12 \) Thus, the final answers are: - Zero(s) of multiplicity one: \( -4 \) - Zero(s) of multiplicity two: \( 11, 12 \)

Quick Answer

Zero(s) of multiplicity one: -4 Zero(s) of multiplicity two: 11, 12
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