Concept explainers
To find the real zeroes of the polynomial function
Answer to Problem 91E
Explanation of Solution
Given:
Function:
Calculation:
The leading coefficient of given polynomial is 1 and the constant term is -4.
So, possible zeroes are:
Using synthetic division to check whether z = 1, is a zero or not.
Here, remainder is not 0. So, z = 1 is not a zero of the given polynomial.
Using synthetic division to check whether z = -1, is a zero or not.
Here, remainder is 0. So, z = -1 is a zero of the given polynomial.
So,
Now, consider
The leading coefficient of above polynomial is 1 and the constant term is -4.
So, possible zeroes are:
Using synthetic division to check whether z = 1, is a zero or not.
Here, remainder is not 0. So, z = 1 is not a zero of the given polynomial.
Using synthetic division to check whether z = 2, is a zero or not.
Here, remainder is 0. So, z = 2 is a zero of the given polynomial.
So,
Now, consider
The above polynomial is a second degree polynomial.
Discriminant
Here, the value of discriminant is less than zero.
So, zeroes does not exists for above second degree polynomial.
Conclusion:
Therefore, the zeroes of given polynomial function are
Chapter 2 Solutions
PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)
- 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