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 - Page 453: 39


{$\frac{1-\sqrt {33}}{4},\frac{1+\sqrt {33}}{4}$}

Work Step by Step

Step 1: Comparing $2y^{2}-y-4=0$ to the standard form of a quadratic equation, $ay^{2}+by+c=0$, we find: $a=2$, $b=-1$ and $c=-4$ 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: $y=\frac{-(-1) \pm \sqrt {(-1)^{2}-4(2)(-4)}}{2(2)}$ Step 4: $y=\frac{1 \pm \sqrt {1+32}}{4}$ Step 5: $y=\frac{1 \pm \sqrt {33}}{4}$ Step 6: $y=\frac{1-\sqrt {33}}{4}$ or $y=\frac{1+\sqrt {33}}{4}$ Step 7: Therefore, the solution set is {$\frac{1-\sqrt {33}}{4},\frac{1+\sqrt {33}}{4}$}.
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