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: 26

Answer

{$1 - i\sqrt 2,1 + i\sqrt 2$}

Work Step by Step

Step 1: Comparing $x^{2}-2x+3=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=1$, $b=-2$ and $c=3$ 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: $x=\frac{-(-2) \pm \sqrt {(-2)^{2}-4(1)(3)}}{2(1)}$ Step 4: $x=\frac{2 \pm \sqrt {4-12}}{2}$ Step 5: $x=\frac{2 \pm \sqrt {-8}}{2}$ Step 6: $x=\frac{2 \pm \sqrt {-1\times8}}{2}$ Step 7: $x=\frac{2 \pm (\sqrt {-1}\times\sqrt {8})}{2}$ Step 8: $x=\frac{2 \pm (\sqrt {-1}\times\sqrt {4\times2})}{2}$ Step 9: $x=\frac{2 \pm (i\times 2\sqrt 2)}{2}$ Step 10: $x=\frac{2 \pm i2\sqrt 2}{2}$ Step 11: $x=\frac{2(1 \pm i\sqrt 2)}{2}$ Step 12: $x=1 \pm i\sqrt 2$ Step 13: $x=1 - i\sqrt 2$ or $x=1 + i\sqrt 2$ Step 14: Therefore, the solution set is {$1 - i\sqrt 2,1 + i\sqrt 2$}.
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.