Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 240: 17



Work Step by Step

If $a$ is a zero of a function with multiplicity $b$ then $(x-a)^b$ is a “multiplier” of the function. The given zeros of the function are: $3\pm2i$ and $4$ with multiplicity $2$. Hence the function could e.g. be: $a(x-(3-2i))(x-(3+2i))(x-4)(x-4)\\=a(x-3-2i)(x-3+2i)(x-4)^2\\=a(x^4-14x^3+77x^2-200x+208).$ If $a=1$, the function is $f(x)=x^4-14x^3+77x^2-200x+208.$ (The degree is $4$ which is good).
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