Solve the following question by using bisection method.
upto six iteration
X³ - X - 11 = 0
Set
Consider when x = 2, then f(2) = -5 < 0
Also, consider when x = 2.5, then f(2.5) = 2.125>0
Since we have that f(2).f(2.5) < 0. We can state that the solution lies in the interval [2,2.5]
Iteration 1:
f(2.25) = -1.8594 < 0
So we replace 2 with 2.25
Iteration 2:
f(2.375) = 0.0215>0
So we replace 2.5 with 2.375
Iteration 3:
f(2.3125) = -0.946 < 0
So, we replace 2.25 with 2.3125
Iteration 4:
f(2.3438) = -0.4684 < 0
So, we replace 2.3125 with 2.3438
Iteration 5:
f(2.3594) = -0.2251 <0
So, we replace 2.3438 with 2.3594
Iteration 6:
f(2.3672) = -0.1023<0
So the solution of is 2.3672 in the interval [2,2.5], using bisection method up to 6 iterations.
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