//bisection method
#include<iostream>
#include<cmath>
#include<iomanip>
using namespace std;
double f(double x);    //declare the function for the given equation
double f(double x)    //define the function here, ie give the equation
{
    double a=pow(x,3)-x-11.0;    //write the equation whose roots are to be determined
    return a;
}
int main()
{    
    cout.precision(4);        //set the precision
    cout.setf(ios::fixed);
    double a,b,c,e,fa,fb,fc;    //declare some needed variables
    a:cout<<"Enter the initial guesses:\na=";    //Enter the value of a(set a label('a:') for later use with goto)
    cin>>a;
    cout<<"\nb=";            //Enter the value of b
    cin>>b;
    cout<<"\nEnter the degree of accuracy desired"<<endl;    //Enter the accuracy
    cin>>e;                //e stands for  accuracy
    if (f(a)*f(b)>0)        //Check if a root exists between a and b
    {                //If f(a)*f(b)>0 then the root does not exist between a and b
        cout<<"Please enter a different intial guess"<<endl;
        goto a;            //go back to 'a' ie 17 and ask for different values of a and b
    }
    else                //else a root exists between a and b
    {
    while (fabs(a-b)>=e)        /*if the mod of a-b is greater than the accuracy desired keep                         bisecting the interval*/
    {
        c=(a+b)/2.0;        //bisect the interval and find the value of c
        fa=f(a);        
        fb=f(b);
        fc=f(c);
        cout<<"a="<<a<<"     "<<"b="<<b<<"     "<<"c="<<c<<"      fc="<<fc<<endl;/*print the                             values of a,b,c and fc  after each iteration*/        
        if (fc==0)        //if f(c)=0, that means we have found the root of the equation
        {
            cout<<"The root of the equation is "<<c;    /*print the root of the equation                                         and break out of the loop*/
            break;
        }

        if (fa*fc>0)    //if f(a)xf(c)>0, that means no root exist between a and c 
        {
            a=c;    /*hence make a=c, ie make c the starting point of the interval and b the                     end point*/
        }
        else if (fa*fc<0)
        {    
            b=c;    /*this means that a root exist between a and c therfore make c the end                     point of the interval*/
        }    
        
    
    }
    }            //The loop ends when the difference between a and b becomes less than the desired accuracy ie now the value stored in 'c' can be called the approximate root of the equation         
    cout<<"The root of the equation is "<<c;    //print the root    
    return 0;    
}
//output attached as jpg

Explanation of the above code:

Manas Sharma

Ph.D. researcher at Friedrich-Schiller University Jena, Germany. I’m a physicist specializing in computational material science. I write efficient codes for simulating light-matter interactions at atomic scales. I like to develop Physics, DFT, and Machine Learning related apps and software from time to time. Can code in most of the popular languages. I like to share my knowledge in Physics and applications using this Blog and a YouTube channel.

manas.bragitoff.com/