Use the bisection method to find √ 2 correct to roughly within 10^−2 . (hint: consider f(x) = x^2 − 2 on [1, 2])

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

We know from the information given that

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

b). 4320 have a nice day