Concept explainers
To verify the upper and lower bounds using synthetic division and to determine the real zeros of the function
Upper bound:
Lower bound:
Answer to Problem 67RE
Explanation of Solution
Given:
Function:
Upper bound:
Lower bound:
Calculation:
- Verifying upper bound:
- Verifying lower bound:
- Calculation of real zeros:
Using synthetic division,
Here, the last row values are positive values or zeros.
Hence, the upper bound of given function is x = 1.
Using synthetic division,
Here, the last row values are alternatively positive and negative.
Hence, the lower bound of given function is
Here, the zeros are calculated using graphical method.
Calculation for graph:
Consider
Values of x | Values of f ( x ) |
0 | -3 |
1 | 2 |
-1 | -14 |
2 | 25 |
-2 | -55 |
By taking different values of x , the graph can be plotted.
Graph:
Interpretation:
By observing graph, it is clear that the curve of the function meets x -axis at
Hence, the zeros of the function are
Conclusion:
Therefore, the zeros of given polynomial function are
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
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- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning