Concept explainers
(a)
To Approximate: the zeros of a function.
(a)

Answer to Problem 96E
Zeros of polynomial are -3.13, -0.452, 3.13 and 0.452.
Explanation of Solution
Given information:
Calculation:
In this theorem the values where sign was changing whose domain lies in the interval contain one zero as at that interval the line of equation intersect the axis and at the point of intersection zeros of polynomial present.
The table for the polynomial
X | h(x) |
-4 | + |
-3 | - |
-2 | - |
-1 | - |
0 | + |
1 | + |
2 | - |
3 | - |
4 | + |
So the signs were change in the interval of (-4,-3) , (-1,0) , (0.1) and (3,4) so the zeros of polynomial are in the intervals.
(b)
To Approximate: the zeros of a function.
(b)

Answer to Problem 96E
Zeros of polynomial are -3.13 , -0.452 , 3.13 and 0.452.
Explanation of Solution
Given information:
Calculation:
Adjusting the interval by 0.1 ,0.01 ,0.001 and 0.0001
x | h(x) |
-3.1 | - |
-3.2 | + |
x | h(x) |
-3.12 | - |
-3.13 | + |
x | h(x) |
-3.130 | - |
-3.131 | + |
x | h(x) |
-3.1300 | - |
-3.1301 | + |
So one zero of polynomial is -3.13
Similarly for the interval (-1,0) , (0.1) and (3,4) the other three zeros are -0.452 , 0.452 and 3.13.
Chapter 2 Solutions
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