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: 29

Answer

{$\frac{(-1 - i\sqrt {5})}{6},\frac{(-1 + i\sqrt {5})}{6}$}

Work Step by Step

Step 1: Comparing $6x^{2}+2x+1=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=6$, $b=2$ 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: $x=\frac{-(2) \pm \sqrt {(2)^{2}-4(6)(1)}}{2(6)}$ Step 4: $x=\frac{-2 \pm \sqrt {4-24}}{12}$ Step 5: $x=\frac{-2 \pm \sqrt {-20}}{12}$ Step 6: $x=\frac{-2 \pm \sqrt {-1\times20}}{12}$ Step 7: $x=\frac{-2 \pm (\sqrt {-1}\times\sqrt {4\times5})}{12}$ Step 8: $x=\frac{-2 \pm (i\times 2\sqrt {5})}{12}$ Step 9: $x=\frac{2(-1 \pm i\sqrt {5}}{12}$ Step 10: $x=\frac{(-1 \pm i\sqrt {5}}{6}$ Step 11: $x=\frac{(-1 - i\sqrt {5})}{6}$ or $x=\frac{(-1 + i\sqrt {5})}{6}$ Step 12: Therefore, the solution set is {$\frac{(-1 - i\sqrt {5})}{6},\frac{(-1 + i\sqrt {5})}{6}$}.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.