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2 Answers

1 votes
1 votes
For bisection method: we have :

f(1) = 1-1-1= -1 similarly, f(2) = 2^4 -2 -1 = 13

root lies between 1 and 2.

First Iteration x1 = (1+2)/2 = 1.5  f(1.5) = 2.5625

IInd iternation x2 = (1+1.5)/2 = 1.25 f(1.25) = .19140625 >0

Hence, root may lie in between (1, 1.25)

Option B is correct.
1 votes
1 votes
Given data.
root= X4-X-1.
Root lies Between 1 and 2,
After second iteration=?
Using bisection method.
f(1)=X4-X-1
=1-1-1
= -1
f(2)=X4-X-1
= 24 -2 -1
=13
Given constraint that “root lies between 1 and 2”
Iteration-1: x1=(a+b)/2
=(1+2)/2
= 1.5
f(1.5) = 2.5625
Iteration-2: x2=(a+b)/2
=(1+1.5)/2
=1.25
f(1.25)=0.19140625 >0
Root may lie in between (1, 1.25)
Answer:

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