Intermediate Algebra (12th Edition)

Published by Pearson
ISBN 10: 0321969359
ISBN 13: 978-0-32196-935-4

Chapter 8 - Section 8.2 - The Quadratic Formula - 8.2 Exercises - Page 519: 46

Answer

Choice D; must use the Quadratic Formula

Work Step by Step

The discriminant of a quadratic equation $ax^2+bx+c=0,$ is given by $b^2-4ac$. Thus, the discriminant of the given equation, $ 18x^2+60x+82=0 ,$ is \begin{align*}\require{cancel} & (60)^2-4(18)(82) \\&= 3600-5904 \\&= -2304 .\end{align*} Since the discriminant is negative, then the equation $ 18x^2+60x+82=0 $ has two nonreal complex numbers as solutions or $\text{ Choice D }$. Furthermore, since the discriminant is less than zero, then the given equation CANNOT be solved using the Zero-Factor Property. Hence, the Quadratic Formula must be used.
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