00:01
So in this video we're looking at the bisection method to find the root of this equation here, which is x to about 4 minus x minus 10 equal to 0.
00:07
We've asked us to find up to five iterations and given the interval a is equal to 1 .5 and be equal to 2.
00:13
We've also asked us to construct a table and explain all the steps of the solution.
00:17
And the bi -section method states that if the interval, within the interval a comma b, if f of x which is sign, then there is a root.
00:25
So in this case, the interval is given to be a comma b, which is 1.
00:30
0 .5 comma 2, thought they've given.
00:32
F of x is given to be x to the bar 4 minus x minus 10 as it stands.
00:40
Now applying the first iteration, which would mean applying the values of 1 .5 and 2 within the f of x.
00:47
So you would find that f of x, f of 1 .5 is negative and f of 2 is positive, therefore that it switches between 1 .5 and 2.
00:54
Therefore it indicates that there is a root between 1 .5 and 2.
00:58
Now, for the first iteration, you would actually take the bisection between 1 .5 and 2, which is essentially the midpoint of 1 .5 and 2, you would get x0 to be equal to 1 .75.
01:09
Similarly, with using 1 .75, we would find that f of x value is a negative, and therefore the root has to lie between 1 .75 and 2 because 2 was positive.
01:20
Considering 1 .75 is negative.
01:22
It has to be between 2 and 1 .75.
01:24
Now, the interval is actually shrinking, and we are getting closer to the root.
01:28
X1 would therefore be the bisection between these two values.
01:33
So 1 .75 plus 2 divided 2, which is 1 .875.
01:36
That's the bi -section method.
01:38
So the third iteration would be substituting 1 .875.
01:42
You would get a value positive for this.
01:45
Therefore, it indicates that this value has to be, the root has to be between a negative...