To prove: that a polynomial with real coefficients and odd degree has at least one real zero
Explanation of Solution
Given information: The question is
The conjugates zeroes theorem says that the complex zeroes of a polynomial with real coefficients occur in complex conjugate pairs
Proof: The polynomial of odd degree n as the product of a polynomial of first degree and
By the conjugate zeroes theorem, the even degree polynomial
The coefficient of
The sum conjugate pairs is a real number a, b are real numbers so d must be real number too
Then a polynomial of odd degree with real coefficients has at least one real root
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