Elementary Algebra

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

Chapter 11 - Additional Topics - Chapter 11 Test: 14


{$\frac{3 - i\sqrt {11}}{2},\frac{3 + i\sqrt {11}}{2}$}

Work Step by Step

Step 1: Comparing $x^{2}-3x+5=0$ to the standard form of a quadratic equation, $ax^{2}+bx+c=0$, we find: $a=1$, $b=-3$ and $c=5$ 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: $x=\frac{-(-3) \pm \sqrt {(-3)^{2}-4(1)(5)}}{2(1)}$ Step 4: $x=\frac{3 \pm \sqrt {9-20}}{2}$ Step 5: $x=\frac{3 \pm \sqrt {-11}}{2}$ Step 6: $x=\frac{3 \pm \sqrt {-1\times11}}{2}$ Step 7: $x=\frac{3 \pm (\sqrt {-1}\times\sqrt {11})}{2}$ Step 8: $x=\frac{3 \pm (i\times \sqrt {11})}{2}$ Step 9: $x=\frac{3 \pm i\sqrt {11}}{2}$ Step 10: $x=\frac{3 - i\sqrt {11}}{2}$ or $x=\frac{3 + i\sqrt {11}}{2}$ Step 11: Therefore, the solution set is {$\frac{3 - i\sqrt {11}}{2},\frac{3 + i\sqrt {11}}{2}$}.
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