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 66E
The polynomial has either three positive or one positive and no negative zeros and total number of real zeros either three or one.
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 three variation in sign, so it has either three positive zero or one 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