College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Section 5.5 - The Real Zeros of a Polynomial Function - 5.5 Assess Your Understanding: 27

Answer

The maximum number of real zeros is $4$ The number of positive real zeros is either $2$ or $0$ The number of negative real zeros is either $2$ or $0$

Work Step by Step

The number of zeros of a polynomial can’t be greater than its degree. $1)$ The number of positive real zeros of $f(x) $ either equals the number of variations in the sign of the nonzero coefficients of $f(x)$ or equals that number minus an even integer $2)$ The number of negative real zeros of $f(x)$ either equals the number of variations in the sign of the nonzero coefficients of $f(-x) $ or equals that number minus an even integer. So the maximum number of real zeros here is $4$ Since $$f\left( x\right) =-x^{4}+x^{2}-1 $$ has $2$ variations The number of positive real zeros is either $2$ Or $0$ Since $$ f\left( -x\right) = -x^{4}+x^{2}-1 $$ Has $2$ variations Number of negative real zeros is either $2$ Or $0$
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.