College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.6 - Complex Zeros; Fundamental Theorem of Algebra - 5.6 Assess Your Understanding: 16

Answer

The missing zeros are: $\color{blue}{\bf-i, \space 3+2i, \space \text{and} \space -2-i}$

Work Step by Step

RECALL: If $a+bi$ is a zero of a polynomial function with real number coefficients, then its conjugate $a-bi$ is also a zero of the function. The polynomial function has a degree of $6$. This means it has 6 zeros. Since complex roots come in conjugate pairs, then the missing zeros of the given function are the conjugates of $i, 3-2i, $ and $-2+i$, which are: $\color{blue}{\bf-i, 3+2i, -2-i}$
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