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: 41

Answer

Choice C; should be solved using 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, $ x^2+4x+2=0 ,$ is \begin{align*}\require{cancel} & 4^2-4(1)(2) \\&= 16-8 \\&= 8 .\end{align*} Since the discriminant is positive and is a non-perfect square, then the equation $ x^2+4x+2=0 $ has two irrational numbers as solutions or $\text{ Choice C }$. Furthermore, since the discriminant is a non-perfect square, then the given equation CANNOT be solved using the Zero-Factor Property. Hence, the Quadratic Formula should be used.
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