Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Problem Set 10.3: 8

Answer

{$\frac{-3 - \sqrt 5}{2},\frac{-3 + \sqrt {5}}{2}$}

Work Step by Step

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