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: 2

Answer

$\color{blue}{\left\{-1-i, -1+i\right\}}$.

Work Step by Step

The complex zeros can be found using the quadratic formula, $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$, where $a, b, $ and $c$ are the coefficients of the terms of the trinomial $ax^2+bx+c$. The given function involves a trinomial that has $a=1, b=2,$ and $c=2$. Substitute these values into the quadratic formula to obtain: $x=\dfrac{-2\pm\sqrt{2^2-4(1)(2)}}{2(1)} \\x=\dfrac{-2\pm\sqrt{4-8}}{2} \\x=\dfrac{-2\pm\sqrt{-4}}{2} \\x=\dfrac{-2\pm\sqrt{4(-1)}}{2} \\x=\dfrac{-2\pm 2i}{2} \\x=\dfrac{-2}{2} \pm \dfrac{2i}{2} \\x=-1\pm i$ Thus, the complex zeros of the given function are: $\color{blue}{\left\{-1-i, -1+i\right\}}$.
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