Elementary Algebra

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

Chapter 10 - Quadratic Equations - 10.3 - Quadratic Formula - Concept Quiz 10.3 - Page 453: 9



Work Step by Step

Step 1: We write $-2x^{2}-3x-1=0$ as $2x^{2}+3x+1=0$. Comparing $2x^{2}+3x+1=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain: $a=2$, $b=3$ 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: $x=\frac{-(3) \pm \sqrt {(3)^{2}-4(2)(1)}}{2(2)}$ Step 4: $x=\frac{-3 \pm \sqrt {9-8}}{4}$ Step 5: $x=\frac{-3 \pm \sqrt {1}}{4}$ Step 6: $x=\frac{-3 \pm 1}{4}$ Step 7: $x=\frac{-3-1}{4}$ or $x=\frac{-3+1}{4}$ Step 8: $x=\frac{-4}{4}$ or $x=\frac{-2}{4}$ Step 9: $x=-1$ or $x=\frac{-1}{2}$ Step 10: Therefore, the solution set is {$-\frac{1}{2},-1$}. Therefore, it is true that the solution set consists of two rational numbers.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.