Question

Bisection Method. x ^ 3 - 9x + 1 = 0 up to 2 decimal places.​

Answer 1

Answer:

Here, x

3

−9x+1=0

Let f(x)=x

3

−9x+1

First Iteration:

Here, f(2)=−9<0 and f(4)=29>0

Now, Root lies between x

0

=2 and x

1

=4

x

2

=x

0

−f(x

0

)×

f(x

1

)−f(x

0

)

x

1

−x

0

=2−(−9)×

29−(−9)

4−2

=2.47368

Second Iteration:

Here, f(2.47368)=−6.1264 and f(2)=29>0

Now, Root lies between x

0

=2.47368 and x

1

=4

x

3

=x

0

−f(x

0

)×

f(x

1

)−f(x

0

)

x

1

−x

0

=2.47−(−6.13)×

29−(−6.13)

4−2.47

=2.73989

Third Iteration:

Here, f(2.73989)=−3.09067 and f(4)=29>0

Now, Root lies between x

0

=2.73989 and x

1

=4

x

4

=x

0

−f(x

0

)×

f(x

1

)−f(x

0

)

x

1

−x

0

=2.74−(−3.09)×

29−(−3.09)

4−2.74

=2.86125