Answer:
Using the Bisection Method
Step-by-step explanation:
These are the steps for the Bisection Method:
Suppose we need a root for f(x) = 0 and we have an error tolerance of ε
- Find two numbers a and b at which the function has different signs
- Define
- if
then accept c as the root and stop
- if
then set c as the new b. Otherwise, set c as the new a. return to step 1.
We know from the information given that
- The function is
- ε = 0.01
Applying the steps of the Bisection Method you get:
1. There is a root between [1,2] because:
2. Define
3.
4. Because we set 1.5 as the new b.
The bisection algorithm is detailed in the following table.
Note that after 7 steps we have hence the required root approximation is c = 1.4106
