Precalculus: Mathematics for Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 1305071751
ISBN 13: 978-1-30507-175-9

Chapter 3 - Section 3.5 - Complex Zeros and the Fundamental Theorem of Algebra - 3.5 Exercises - Page 294: 71

Answer

(a) 4 real zeros. (b) 2 real and 2 non-real zeros. (c) 4 non-real zeros.

Work Step by Step

(a) We graph the function as shown in the figure (a). Clearly there are 4 intersection points between the function and the x-axis, indicating 4 real zeros in this case. (b) See graph (b), there are two intersection points between the function and the x-axis, hence, there are 2 real zeros. As it is a 4th order polynomial, there must be 2 non-real zeros as required by the Zeros theorem. (c) See graph (c), the minimum of the function is at $(1.366,39.75)$ and there are no intersection points between the function and the x-axis, indicating that there are no real zeros. According to the Zeros Theorem, there must be 4 non-real zeros.
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.