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: 23

Answer

{$1 - 3i\sqrt 2,1 + 3i\sqrt 2$}

Work Step by Step

Step 1: Comparing $y^{2}-2y+19=0$ to the standard form of a quadratic equation, $ay^{2}+by+c=0$, we find: $a=1$, $b=-2$ and $c=19$ Step 2: The quadratic formula is: $y=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$ Step 3: Substituting the values of a, b and c in the formula: $y=\frac{-(-2) \pm \sqrt {(-2)^{2}-4(1)(19)}}{2(1)}$ Step 4: $y=\frac{2 \pm \sqrt {4-76}}{2}$ Step 5: $y=\frac{2 \pm \sqrt {-72}}{2}$ Step 6: $y=\frac{2 \pm \sqrt {-1\times72}}{2}$ Step 7: $y=\frac{2 \pm (\sqrt {-1}\times\sqrt {72})}{2}$ Step 8: $y=\frac{2 \pm (\sqrt {-1}\times\sqrt {36\times2})}{2}$ Step 9: $y=\frac{2 \pm (i\times 6\sqrt 2)}{2}$ Step 10: $y=\frac{2 \pm 6i\sqrt 2}{2}$ Step 11: $y=\frac{2(1 \pm 3i\sqrt 2)}{2}$ Step 12: $y=1 \pm 3i\sqrt 2$ Step 13: $y=1 - 3i\sqrt 2$ or $y=1 + 3i\sqrt 2$ Step 14: Therefore, the solution set is {$1 - 3i\sqrt 2,1 + 3i\sqrt 2$}.
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