Problem: Here we have to find root for the polynomial x^3-8*x-4 upto 6D(decimal places)
Solution in C:
#include<stdio.h>
#include<math.h>
#define f(x) pow(a,3)-8*a-4;
#define fd(x) 3*pow(a,2)-8;
int main()
{
double a,b,c,d,h,k,x,y;
int i,j,m,n;
printf("Enter the value of xn: ");
scanf("%lf",&a);
printf("Enter itteration number: ");
scanf("%d",&n);
printf(" xn f(x) f'(x) hn=-f(x)/f'(xn) xn+1=xn+h\n");
printf("-----------------------------------------------------------------------------------------\n");
for(i=1;i<=n;i++)
{
x=f(a);
y=fd(x);
h=-(x/y);
k=h+a;
printf(" %.7lf %.7lf %.7lf %.7lf %.7lf\n",a,x,y,h,k);
a=k;
}
printf("\nThe approximation to the root is %.6lf which is upto 6D",k);
return 0;
}
Output:
