College Algebra (10th Edition)

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

Chapter 1 - Section 1.3 - Complex Numbers; Quadratic Equations in the Complex Number System - 1.3 Assess Your Understanding: 64

Answer

$\displaystyle -\frac{3}{10}\pm\frac{1}{10}i$

Work Step by Step

$10x^{2}+6x+1=0$ We solve using the quadratic formula ($a=10,\ b=6,\ c=1$): $\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$ $\displaystyle x=\frac{-6\pm\sqrt{6^{2}-4(10)(1)}}{2(10)}$ $\displaystyle x=\frac{-6\pm\sqrt{36-40}}{2(10)}$ $\displaystyle x=\frac{-6\pm\sqrt{-4}}{20}$ $\displaystyle x=\frac{-6\pm 2i}{20}=-\frac{3}{10}\pm\frac{1}{10}i$ Recall, $i=\sqrt{-1}$
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