Concept explainers
To find:how many positive and how many negative real zeros the polynomial have using Descartes’s rule of sign and determine the possible total number of real zeros.
Answer to Problem 68E
The polynomial has 0 positive andeither four or two negative zeros and total number ofeither twoor four real zeros .
Explanation of Solution
Given information:
The polynomial is
Concept used: Descartes’s rule of signs:
Let P be a polynomial with real coef?cients.
1. The number of positive real zeros of
2. The number of negative real zeros of
Calculation:
The polynomial has no variation in sign, so it has 0 positive zeros, now
So,
Thus,
Chapter 3 Solutions
Precalculus: Mathematics for Calculus - 6th 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