Concept explainers
(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 21WE
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
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