Trigonometry (11th Edition) Clone

Published by Pearson
ISBN 10: 978-0-13-421743-7
ISBN 13: 978-0-13421-743-7

Chapter 8 - Test - Page 412: 4


{$\frac{1}{4}\pm\frac{\sqrt {31}}{4}i$}

Work Step by Step

We will use the quadratic formula to solve the equation over a set of complex numbers. Step 1: Comparing $2x^{2}-x+4=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$; $a=2$, $b=-1$ and $c=4$ Step 2: The quadratic formula is: $x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a,b and c in the formula: $x=\frac{-(-1) \pm \sqrt {(-1)^{2}-4(2)(4)}}{2(2)}$ Step 4: $x=\frac{1 \pm \sqrt {1-32}}{4}$ Step 5: $x=\frac{1 \pm \sqrt {-31}}{4}$ Step 6: $x=\frac{1 \pm \sqrt {-1\times31}}{4}$ Step 7: $x=\frac{1 \pm (\sqrt {-1}\times\sqrt {31})}{4}$ Step 8: As $i=\sqrt {-1}$, the equation becomes: $x=\frac{1 \pm (i\times \sqrt {31})}{4}$ Step 9: $x=\frac{1 \pm i\sqrt {31}}{4}$ Step 10: $x=\frac{1}{4}\pm\frac{\sqrt {31}}{4}i$ Step 11: Therefore, the solution set is {$\frac{1}{4}\pm\frac{\sqrt {31}}{4}i$}.
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