00:01
Hi, in this question consider the function given that is f of x which is equal to x cube plus x minus 4 in the interval 1 comma 4.
00:13
We have to solve this by the bisection method.
00:16
Now we'll say that consider a few values of x that is 1, 2, 3 and 4 which lies in this interval.
00:24
So finding the values of f of x so that will be minus 2.
00:29
Year we get six, year it is 26 and year we get it as 64.
00:34
Now we'll start with the first iteration.
00:38
So in the first iteration we have f of 1, it is less than 0 and we get f of 2 it is greater than 0.
00:47
We have x not to be equal to 1 .5 and we have f of x not.
00:53
That means f of 1 .5 to be equal to 0 .875 which is greater than 0.
01:02
Now further we'll move ahead and start with the second iteration.
01:07
So in the second iteration we have f of 1 it is equal to less than 0 and we have f of 1 .5 to be greater than 0.
01:18
So we have x1 to be equal to 1 .25 and then f of x1 we get it as minus 0 .7969 which is less than 0.
01:31
Now with the third iteration we get this as f of 1 .25 it is less than 0 and f of 1 .5 it is greater than 0.
01:46
We have x2 as 1 .375.
01:51
So f of x2 will be equal to minus 0 .0254, that is less than 0.
01:59
Then we'll say that we'll start with the fourth iteration here.
02:04
So in the fourth iteration, we have f of 1 .375, it is less than 0...