Concept explainers
To write: A polynomial function
Answer to Problem 3CFU
This function either has:
3 or 1 positive real zeros,
0 negative real zeros,
2 or 0 imaginary zeros
Explanation of Solution
Given information: A polynomial function
Calculation:
Function that we made up
Pay attention to the signs in front of each term. Each time a sign changes from + to − or vice versa that counts as 1 change.
3 sign changes = 3 or 1
They have asked for 3 sign changes and they are:
However many # of changes you find, there is also a possibility of two less than that number
Now do
Note there are no sign changes for this function.
0 sign change = There are 0 negative real zeros.
The degree of the function is 3, so we know there are 3 zeros possible.
These are the only possible combinations given what we just found
* 3 positive real zeros, 0 negative real zero, 0 imaginary zeros.
* 1 positive real zero, 0 negative real zero, 2 imaginary zeros.
This function either has:
3 or 1 positive real zeros,
0 negative real zeros,
2 or 0 imaginary zeros
Chapter 4 Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Additional Math Textbook Solutions
Calculus: Early Transcendentals (2nd Edition)
Single Variable Calculus: Early Transcendentals (2nd Edition) - Standalone book
Calculus: Early Transcendentals (3rd Edition)
University Calculus: Early Transcendentals (4th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
University Calculus: Early Transcendentals (3rd Edition)
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning