Concept explainers
(a)
To calculate: The interval in which the zeros of polynomial are.
(a)
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Answer to Problem 35CR
The intervals are (-3,-2), (-1, 0) and (0, 1)
Explanation of Solution
Given information:
Calculation:
Intermediate value theorem states that if a continuous function takes two values say
By this theorem we can say that if at one point the function is having a positive value and at other point it is having a negative value then between those intervals have a zero of the polynomial.
The table for the polynomial
x | F(x) |
-3 | - |
-2 | + |
-1 | + |
0 | - |
1 | + |
2 | + |
The interval are (-3,-2), (-1, 0) and (0,1)
(b)
To calculate: Zeros of the polynomial to nearest thousand.
(b)
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Answer to Problem 35CR
The zeros of polynomial are: -2.247, -0.555 and 0.802.
Explanation of Solution
Given information:
The intervals are (-3,-2), (-1, 0) and (0, 1)
Calculation:
a) Adjusting the interval by 0.1 ,0.01 and 0.001
x | F(x) |
-2.3 | - |
-2.2 | + |
x | F(x) |
-2.25 | - |
-2.24 | + |
x | f(x) |
-2.248 | - |
-2.247 | + |
So one zero of polynomial is -2.247
Similarly for the interval (-1, 0) and (0, 1) the other two zeros are -0.555 and 0.802.
Chapter 2 Solutions
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