Elementary Algebra

Published by Cengage Learning
ISBN 10: 1285194055
ISBN 13: 978-1-28519-405-9

Chapter 11 - Additional Topics - 11.5 - Quadratic Equations: Complex Solutions - Problem Set 11.5: 20

Answer

{$\frac{-1 - i\sqrt {7}}{4},\frac{-1 + i\sqrt {7}}{4}$}

Work Step by Step

Step 1: Comparing $2x^{2}+x+1=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=2$, $b=1$ and $c=1$ 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: $x=\frac{-(1) \pm \sqrt {(1)^{2}-4(2)(1)}}{2(2)}$ Step 4: $x=\frac{-1 \pm \sqrt {1-8}}{4}$ Step 5: $x=\frac{-1 \pm \sqrt {-7}}{4}$ Step 6: $x=\frac{-1 \pm \sqrt {-1\times7}}{4}$ Step 7: $x=\frac{-1 \pm (\sqrt {-1}\times\sqrt {7})}{4}$ Step 8: $x=\frac{-1 \pm (i\times \sqrt {7})}{4}$ Step 9: $x=\frac{-1 \pm i\sqrt {7}}{4}$ Step 10: $x=\frac{-1 - i\sqrt {7}}{4}$ or $x=\frac{-1 + i\sqrt {7}}{4}$ Step 11: Therefore, the solution set is {$\frac{-1 - i\sqrt {7}}{4},\frac{-1 + i\sqrt {7}}{4}$}.
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