Question

find the positive
root
of x-cosx=0 correct
to 4
decimal by
bisection
Method​

Answer 1

ANSWER

f (1) =13

– 1 – 1 = –1, which is negative

f (2) = 23

– 2 – 1 = 5, which is positive

  A root of f (x) = x

3

– x – 1 = 0 lies in between 1 and 2.

  x1 =

(1 2) 3

2 2

  = 1.5

f (x1) = f (1.5) = (1.5)3

– 1.5 – 1 = 0.875, which is positive.

Hence, the root lies in between 1 and 1.5

  x2 =

(1 1.5)

2



= 1.25

f (x2) = f (1.25) = (1.25)3

– 1.25 – 1 = – 0.29, which is negative.

Hence, the root lies in between 1.25 and 1.5

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