Question

Find the root of the equation x^3-2x-5= 0 by Bisection method correct up to three decimal places.

Answer 1

find the root of the equation

Answer 2

Given :    x³ -  2x  - 5  = 0  

To find :  root of the equation  by Bisection method correct up to three decimal places

Solution:

x³ -  2x  - 5  = 0

x = 1  => 1  - 2 - 5  = - 6

x = 2 => 8 - 4 -  5 = - 1

x = 3 =>  27 - 6 - 5 = 16

0 lies between -1  & 16

Hence x lies between 2 & 3

(2 + 3)/2 = 2.5

x = 2.5  =>     x³ -  2x  - 5  = 5.625

0 lies between -1  & 5.625

=> x lies between 2  &  2.5

(2 + 2.5)/2 = 2.25

x = 2.25  =>  x³ -  2x  - 5  = 1.89

0 lies between -1  & 1.89

=>  x lies between 2  &  2.25

=> x = 2.125  => x³ -  2x  - 5  = 0.34

0 lies between -1  & 0.34

=> x lies between 2  * 2.125

=> x = 2.0625   => x³ -  2x  - 5  = -0.35

0 lies between  -0.35 & 0.34

=> x lies between  2.0625   & 2.125

x = 2.09375    => x³ -  2x  - 5  =    -0.0089 ≈  0

x =  2.094    up to three decimal places

x =  2.094  

Learn more:

Show the function f of x is equal to x cube minus 3 x square + 6 x ...

https://brainly.in/question/8910323

a+b+c=3 a^2+b^2+c^2=6 1/a+1/b+1/c=1 find values of a , b and c

https://brainly.in/question/8061154