Concept explainers
To find : the rational zeros of the given function
Answer to Problem 103E
The rational zeros of the function are:
Explanation of Solution
Given information:
Concept Involved:
The zeros of the polynomial are the values of x where the graph cuts the x-axis and makes
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:
To find the zeros of the function set the polynomial equal to zero
To get rid of the fraction in the equation multiply 4 throughout the equation
Identify two numbers in such a way that their product (ac) is 144 and sum (b) is -25 by listing out the factor pairs of 144 and see which two add up to give -25.
Factor the GCF of first two terms and GCF of last two terms in left side of the equation
Factor the common binomial from left side of the equation
Rewrite the binomials inside each parenthesis
Use the algebraic identity
We need to set each factor equal to zero using the zero factor property which states that
“If
Solving the 1st equation
- By subtracting 2 on both sides
- By simplifying the equation on both sides
Solving the 2nd equation
- By adding 2 on both sides
- By simplifying the equation on both sides
Solving the 3rd equation
- By subtracting 3 on both sides, then
- By simplifying on both sides, then
- By dividing 2 on both sides, and then
- By simplifying fraction on both sides
Solving the 4thequation
- By adding 3 on both sides, then
- By simplifying on both sides, then
- By dividing 2 on both sides, and then
- By simplifying fraction on both sides
Graph:
Conclusion:
The rational zeros of the function 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