Concept explainers
a.
To find the zeros of the function
a.
Answer to Problem 111RE
Explanation of Solution
Given:
Function:
Calculation:
- Performing rational zero test:
- Finding rational zeros:
The leading coefficient of given polynomial is 1 and the constant term is -4.
So, possible rational zeros are:
Using synthetic division to check whether x = 2, is a zero or not.
Here, remainder is 0. So, x = 2 is a zero of the given polynomial.
So,
Now, consider
The above polynomial is a second degree polynomial.
So, zeroes of a second degree polynomial can be found using the formula
Conclusion:
Therefore, the zeros of given polynomial function are
b.
To write the factors of the function
b.
Answer to Problem 111RE
Explanation of Solution
Given:
Function:
Calculation:
From above answers, the polynomial as a product of linear factors is
Conclusion:
Therefore,
c.
To find the x - intercepts of the function
c.
Answer to Problem 111RE
Explanation of Solution
Given:
Function:
Calculation:
To find x - intercepts, put
Calculation for graph:
Consider
Values of x | Values of f ( x ) |
0 | -4 |
1 | -1 |
-1 | -15 |
2 | 0 |
-2 | -40 |
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 x - intercept of the function is
Here,
Conclusion:
Therefore, the x - intercept of given function is
Chapter 2 Solutions
Precalculus with Limits: A Graphing Approach
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