Perform three iteration of the bisection method compute the positive root of
the equation f(x) = x2 – 5x + 2.
Answers
Step-by-step explanation:
Perform three iteration of the bisection method compute the positive root of
the equation f(x) = x2 – 5x + 2.
Given : x²- 5x + 2
To find : root of the equation by Bisection method
Solution:
x²- 5x + 2 = 0
x = 0 => 0 - 0 + 2 = 2
x = 1 => 1 - 5 + 2 = - 2
0 lies between 2 and - 2
Hence x lies between 0 and 1
(0 + 1)/2 = 0.5
x = 0.5 => 0.5² - 5(0.5) + 2 = -0.25
0 lies between -0.25 and 2
=> x lies between 0 and 0.5
(0+ 0.5)/2 = 0.25
Keep repeating this process
0 2
1 -2
0.5 -0.25
0.25 0.8125
0.375 0.265625
0.4375 0.00390625
0.46875 -0.124023438
0.453125 -0.060302734
0.4453125 -0.028259277
0.44140625 -0.012191772
0.439453125 -0.004146576
0.438476563 -0.000121117
0.437988281 0.001892328
0.438232422 0.000885546
0.438354492 0.0003822
0.438 is the required root
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