Concept explainers
To find : the possible rational zeros of the given function
Answer to Problem 18E
The possible rational zeros of the function are:
The actual rational zeros of the function in the graph are:
Explanation of Solution
Given information :
Concept Involved:
The Rational Zero Test : The Rational Zero Test relates the possible rational zeros of a polynomial (havinginteger coefficients) to the leading coefficient and to the constant term of the polynomial.
If the polynomial
To use the Rational Zero Test, you should first list all rational numbers whosenumerators are factors of the constant term and whose denominators are factors of theleading coefficient.
Possible rational zeros:
Synthetic Division (for a Cubic Polynomial): To divide
In case when we have a polynomial with a missing term, insert placeholders with zero coefficients for missing powers of the variable. Vertical pattern: Add terms in columns Diagonal pattern: Multiply results by k. This algorithm for synthetic division works only for divisors of the form x - k. Remember that |
The Division Algorithm : If
Calculation:
Identifying the constant and leading coefficient of the given function
Constant is -2
Leading coefficient is 4
Listing the factors of constant -2:
Listing the factors of Leading Coefficient 4:
The possible rational zeros of the function are:
Checking whether
Since we get 0 as our remainder when using -1 during synthetic division
Checking whether
Since we get 0 as our remainder when using 1 during synthetic division
Checking whether
Since we get 0 as our remainder when using
Checking whether
Since we get 0 as our remainder when using
Checking whether
Since we get 0 as our remainder when using
Conclusion:
The possible rational zeros of the function are:
The actual rational zeros of the function in the graph are:
Chapter 2 Solutions
EBK PRECALCULUS W/LIMITS
- 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