(a).
To verify: the given value of m is between P ( a ) and P ( b ) for the given polynomial P .
(a).
Explanation of Solution
Given:
The polynomial:
The values of a , b , and m :
Formula Used:
Intermediate-Value Theorem:
If P is a polynomial function with real coefficients, and m is any number between P (a) and P ( b ), then there is at least one number c between a and b for which P ( c ) = m .
Proof:
As per the given problem
The polynomial:
For
For
Therefore,
(b)
To find: the number c between a and b such that
(b)
Answer to Problem 22WE
Explanation of Solution
Given:
The polynomial:
The values of a , b , and m :
Concept Used:
Intermediate-Value Theorem:
If P is a polynomial function with real coefficients, and m is any number between P (a) and P ( b ), then there is at least one number c between a and b for which P ( c ) = m .
Calculation:
As per the given problem
As
For P ( c ) = m
As c lies between
Therefore,
Chapter 8 Solutions
Algebra and Trigonometry: Structure and Method, Book 2
Additional Math Textbook Solutions
College Algebra (6th Edition)
Intermediate Algebra (7th Edition)
Algebra and Trigonometry
Linear Algebra and Its Applications (5th Edition)
College Algebra with Modeling & Visualization (6th Edition)
Graphical Approach To College Algebra
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education