Question

Formula of Bisection method is(MCQ)


x=a+b/2

x=a-b/2

x=a*b/2

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Answer 1

Answer:

x=a+b/2

is the correct answer

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Answer 2

Formula of Bisection method is   x=(a+b)/2

Bisection method

This method is used to find root a function.

Assume that There is a function f(x)

f(a) and f(b) are opposite sign

There Exists a root between a and b

Using bisection method Mean of a and b  taken

x = (a + b)/2

now check f((a+b)/2) .

Check sign of f((a+b)/2)

And find next mean between (a + b)/2 and a/b depending upon opposite signs .

This Process is keep continued untill f(x) = 0 or with in allowable approximation/error limits.

Hence,  Formula of Bisection method is   x=(a+b)/2

Understand with an example

f(x) = x² - 2

f(0) = - 2

f(1) = - 1

f(2) = 2

f(1) and f(2) of opposite signs hence a root lie between 1 and 2

Mean of 1 and 2 = 3/2

f(3/2) = 1/4

f(1) and f(3/2) are of opposite signs hence a root lie between 1 and 3/2

Mean of 1 and 3/2  = 5/4

f(5/4) = -7/4

f(3/2) and (5/4) are of opposite sign  hence a root lie between 5/4 and 3/2

Mean of 5/4 and 3/2  = 11/8

Continue this process until f(x) ≈ 0

x f(x)

1 -1

2 2

1.5 0.25

1.25 -0.4375

1.375 -0.109375

1.4375 0.06640625

1.40625 -0.022460938

1.421875 0.021728516

1.4140625 -0.000427246

1.41796875 0.010635376

1.416015625 0.00510025

1.415039063 0.002335548

1.414550781 0.000953913

1.414306641 0.000263274

1.41418457 -8.20011E-05

1.414245605 9.06326E-05

1.414215088 4.31482E-06

x ≈ 1.4142