Mehedi

#include<iostream>
#include<math.h>
#include<conio.h>
using namespace std;

#define f(x) (x*x)+x-2
#define E 0.00001
int main()
{
    float x1,x2,f0,f1,f2,x0,root;
    int i=1;
    cout<<"Enter two limits: ";
    cin>>x1>>x2;
    f1=f(x1);
    f2=f(x2);
    if(f1*f2>0)
    {
        cout<<"x1 &x2 do not bracket any root";
        goto stop;
    }
    while (1)
    {
        x0=x1-((f1*(x2-x1))/(f2-f1));
        f0=f(x0);
        if(f1*f0<0)
        {
            x2=x0;
            f2=f0;
        }

        else{
            x1=x0;
            f1=f0;
        }
        cout.precision(6);
        cout<<"\nIteration " <<i <<"\t"<<fixed<<x1<<"\t\t"<<fixed<<x2;

    if (fabs((x2-x1)/x2)<E)
    {
        root = (x1+x2)*0.5;
        cout.precision(6);
        cout<<"\n\nFinal iteration "<<i+1<<"\tRoot = "<<fixed<<root;
        goto stop;

    }
    else
        i++;
    }

    stop:
        getch();

    return 0;
}

newton

#include<iostream>
#include<math.h>
using namespace std;

#define E 0.000001
#define MAX 20
#define F(x) (x*x)+x-2
#define FD(x) 2*x+1

int main()
{
    float x0,xn,fx,fdx,fv;
    int i=1;
    cout<<"Input initial value of x"<<endl;
    cin>>x0;
    cout<<"SOLUTION BY NEWTON-RAPHSON METHOD"<<endl;
    m3014:
        fx=F(x0);
        fdx = FD(x0);
        xn=x0-fx/fdx;
        fv = F(xn);

        if(fabs((xn-x0)/xn)<E)
        {
            cout.precision(7);
            cout<<"Root = "<<fixed<<xn<<endl;
            cout.precision(7);
            cout<<"Function value = "<<fixed<<fv<<endl;
            cout<<"Number of iteration = "<<i<<endl;
        }
        else{
            x0 = xn;
            i++;
            if(i<MAX)
                goto m3014;
            else{
                cout<<"SOLUTION DOES NOT CONVERGE"<<endl;
                cout<<"IN "<<MAX<<" ITERATIOMS"<<endl;
            }
        }
    return 0;
}