Question

Perform five iterations of bisection method to
obtain the smallest positive root of equation
f(x) = x3 - 5x + 1 = 0
I​

Answer 1

Given : f(x) = x³ - 5x + 1  = 0

To Find : Smallest positive root of equation using bisection method

Solution:

f(x) = x³ - 5x + 1  = 0

f(0) =  1

f(1)  = -3

root lies between 0 & 1  

f(0.5) = -1.375

root lies between 0 &  0.5

f(0.25) = -0.234375

root lies between 0 &  0.25

f(0.125) =  0.376953125

root lies between 0.125 & 0.25

f(0.1875) = 0.069091797

root lies between 0.1875 & 0.25

f(0.21875) = -0.083282471

root lies between 0.1875 and 0.21875

f(0.203125)= -0.00724411

root lies between 0.203125 & 0.1875

f(0.1953125) = 0.030888081

root lies between 0.1953125 & 0.203125

f(0.19921875) = 0.011812866

root lies between 0.19921875 and 0.203125

f(0.201171875) = 0.002282076

root lies between 0.201171875 and 0.203125

f(0.202148438)= -0.002481596

root lies between 0.201171875 and 0.202148438

f(0.201660156) -9.99043E-05

Hence 0.20166   is the smallest positive root of equation x³ - 5x + 1  = 0

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