Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.6 - Rational Expressions - Exercise Set - Page 87: 123


The value of the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ for $a=2,b=9,\text{ and }c=-5$ is $-5$.

Work Step by Step

Consider the expression, $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ Now, substitute the value $a=2,b=9,\text{ and }c=-5$ in the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ Therefore, $\begin{align} & \frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}=\frac{-9-\sqrt{{{\left( 9 \right)}^{2}}-4\cdot 2\cdot \left( -5 \right)}}{2\cdot 2} \\ & =\frac{-9-\sqrt{81+40}}{4} \\ & =\frac{-9-\sqrt{121}}{4} \\ & =\frac{-9-11}{4} \end{align}$ Further simplify, $\begin{align} & \frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}=\frac{-20}{4} \\ & =-5 \end{align}$ Therefore, the value of the expression $\frac{-b-\sqrt{{{b}^{2}}-4ac}}{2a}$ for $a=2,b=9,\text{ and }c=-5$ is $-5$.
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