Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter R - Algebra Reference - R.4 Equations - R.4 Exercises - Page R-16: 22


$\displaystyle \frac{4+\sqrt{6}}{5}\approx 1.290$ $\displaystyle \frac{4-\sqrt{6}}{5}\approx 0.310$

Work Step by Step

$5x^{2}-8x+2=0$ Use the quadratic formula: (For $ax^{2}+bx+c=0,\ x=\displaystyle \frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ ) $x=\displaystyle \frac{-(-8)\pm\sqrt{(-8)^{2}-4(5)(2)}}{2(5)}$ $=\displaystyle \frac{8\pm\sqrt{24}}{10}=\frac{8\pm\sqrt{4\times 6}}{10}$ $=\displaystyle \frac{8\pm 2\sqrt{6}}{10}=\frac{2(4\pm\sqrt{6})}{2(5)}$ $x=\displaystyle \frac{4\pm\sqrt{6}}{5}$ Solutions: $\displaystyle \frac{4+\sqrt{6}}{5}\approx 1.290$ and $\displaystyle \frac{4-\sqrt{6}}{5}\approx 0.310$.
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