Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 11 - Quadratic Functions and Equations - 11.2 The Quadratic Formula - 11.2 Exercise Set - Page 713: 20


$t=-5+i$ or $t=-5-i$

Work Step by Step

$ t^{2}+10t+26=0\qquad$... solve with the Quadractic formula. $a=1,\ b=10,\ c=26$ $ t=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\qquad$... substitute $b$ for $10,\ a$ for $1$ and $c$ for $26$. $ t=\displaystyle \frac{-10\pm\sqrt{(10)^{2}-4\cdot(26)\cdot 1}}{2\cdot 1}\qquad$... simplify. $t=\displaystyle \frac{-10\pm\sqrt{100-104}}{2}$ $ t=\displaystyle \frac{-10\pm\sqrt{-4}}{2}\qquad$... write in terms of $i$. ($\sqrt{-1}=i$) $t=\displaystyle \frac{-10\pm 2i}{2}$ $ t=-5\pm i\qquad$... the symbol $\pm$ indicates two solutions. $t=-5+i$ or $t=-5-i$
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