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 68RE
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 = 8.
Using synthetic division,
Here, the last row values are alternatively positive and negative.
Hence, the lower bound of given function is x = -4.
Here, the zeros are calculated using graphical method.
Calculation for graph:
Consider
Values of x | Values of f ( x ) |
0 | 8 |
1 | -9 |
-1 | 15 |
2 | -24 |
-2 | 0 |
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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