Concept explainers
(a)
The real zeros of the polynomial function
(a)
Answer to Problem 47E
The real zeroes for the given function do not exist.
Explanation of Solution
Given information:
The given function
Formula used:
The real zeroes of the polynomial function by putting
Calculation:
It can be shown that for a polynomial function f of degree n, the following statements are true.
(1) The function has at most n real zeroes
(2) The graph of f has, at most n-1 turning points.
We can determine the real zeroes of the polynomial function by putting
So, the real zeroes for the given function does not exist.
Hence, the graph of the polynomial function does not touch x-axis.
Conclusion:
The real zeroes for the given function do not exist.
(b)
The multiplicity of each zero is even or odd.
(b)
Answer to Problem 47E
The multiplicity of each zero is odd
Explanation of Solution
Given information:
The given function
Formula used:
There is only one turning point.
Calculation:
It can be shown that for a polynomial function f of degree n, the following statements are true.
(1) The function has at most n real zeroes
(2) The graph of f has, at most n-1 turning points.
The degree of the given polynomial function is 4. So, there will be at most three turning pointsbut as there is no real zero so there will be only one turning point.
Hence, there is only one turning point.
Conclusion:
There is only one turning point.
(c)
The maximum possible number of turning points.
(c)
Answer to Problem 47E
The graph that there are no real zeroes of the polynomial functions and thereis only one turning point.
Explanation of Solution
Given information:
The given function
Formula used:
The graph is plotted against x axis and y axis.
Calculation:
It can be shown that for a polynomial function f of degree n, the following statements are true.
(1) The function has at most n real zeroes
(2) The graph of f has, at most n-1 turning points.
Let us draw the graph of the given polynomial function,
We can observe from the graph that there are no real zeroes of the polynomial function and thereis only one turning point.
Conclusion:
The graph that there are no real zeroes of the polynomial functions and thereis only one turning point.
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