Concept explainers
(a)
The real zeros of the polynomial function
(a)
Answer to Problem 41E
The real zeroes of the polynomial function are at
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 are
Hence, the real zeroes of the polynomial function are at
Conclusion:
The real zeroes of the polynomial function are at
(b)
The multiplicity of each zero is even or odd.
(b)
Answer to Problem 41E
The multiplicity is odd and there are two turning points.
Explanation of Solution
Given information:
The given function
Formula used:
The multiplicity of each zero is odd
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 3. So, there will be at most two turning points and multiplicity of each zero is odd.
Hence, the multiplicity is odd and there are two turning points.
Conclusion:
The multiplicity is odd and there are two turning points.
(c)
The maximum possible number of turning points.
(c)
Answer to Problem 41E
There are two turning points.
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 the zeroes of the polynomial function are at x = 0 and
Conclusion:
The zeroes of the polynomial function are at x = 0 and
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