Elementary Algebra

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

Chapter 11 - Additional Topics - Chapter 11 Test - Page 521: 12


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

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: $x=\frac{2 \pm \sqrt {-1\times4\times2}}{2}$ Step 7: $x=\frac{2 \pm (\sqrt {-1}\times\sqrt 4\times\sqrt 2)}{2}$ Step 8: $x=\frac{2 \pm (i\times 2\times\sqrt 2)}{2}$ Step 9: $x=\frac{2 \pm 2i\sqrt 2}{2}$ Step 10: $x=\frac{2(1 \pm i\sqrt 2)}{2}$ Step 11: $x=1 \pm i\sqrt 2$ Step 12: $x=1- i\sqrt 2$ or $x=1+ i\sqrt 2$ Step 13: Therefore, the solution set is {$1- i\sqrt 2,1+i\sqrt 2$}.
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