Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 3 - Polynomial and Rational Functions - Section 3.3 Complex Zeros; Fundamental Theorem of Algebra - 3.3 Assess Your Understanding - Page 231: 17



Work Step by Step

Let us consider that $a$ is a zero of a function with multiplicity $b$. Then this factor of the function can be expressed as: $(x-a)^b$. We are given that the zeros of the function are: $3\pm2i$ and $4$ with multiplicity $2$. Therefore, we can write the equation of the function as: $f(x)=[x-(3-2i)][x-(3+2i)](x-4)(x-4)\\=(x-3-2i)(x-3+2i)(x-4)^2\\=x^4-14x^3+77x^2-200x+208$
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