Algebra and Trigonometry 10th Edition

Published by Cengage Learning
ISBN 10: 9781337271172
ISBN 13: 978-1-33727-117-2

Chapter 1 - 1.5 - Complex Numbers - 1.5 Exercises - Page 120: 71

Answer

$\frac{ - 4\pm i\sqrt {5} }{2}$

Work Step by Step

The quadratic formula says $x = \frac{ - b \pm \sqrt {b^2 - 4ac} }{2a}$ when $ax^2 + bx + c = 0$. We know that $i^2=-1$. Hence here $x = \frac{ - 16 \pm \sqrt {16^2 - 4\cdot4\cdot21} }{2\cdot4}= \frac{ - 16 \pm \sqrt {256 - 336} }{8}= \frac{ - 16 \pm \sqrt {-80} }{8}= \frac{ - 16 \pm 4i\sqrt {5} }{8}= \frac{ - 4\pm i\sqrt {5} }{2}$
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