#include <stdio.h>
#include <math.h>
#include <assert.h>
 
double f (double x){
  /* (x - 5.0) * (x - 3.0) * (x + 7.0) */
  return (x*x*x - x*x - 41.0 * x + 105.0);
}

int sameSign(double x, double y){
  return x * y >= 0.0;
}

double middleOf(double x, double y){
  return x + (y - x)/2;
}

int isSmallNumber(double x){
  return (fabs(x) < 0.0000001);
}   

double findRootBetween(double l, double u){
 double res;
 assert(l <= u); assert(!sameSign(f(l), f(u))); 
 while (!isSmallNumber(f(middleOf(l,u)))){ 
   if(sameSign(f(middleOf(l,u)), f(u)))
     u = middleOf(l,u);
   else 
     l = middleOf(l,u);
 }
 res = middleOf(l,u);
 assert(isSmallNumber(f(res)));
 return res;
}     

int main (void){
    double x, y;
    int numbers; 

    do{
      printf("%s","Find a ROOT between which numbers: ");
      numbers = scanf("%lf%lf", &x, &y);

      if (numbers == 2 && !sameSign(f(x),f(y))){
          double solution = findRootBetween(x,y);
          printf("\nThere is a root in %lf\n", solution);
        }
      else if (numbers == 2 && sameSign(f(x),f(y)))
          printf("\nf must have different signs in %lf and %lf\n",
                  x, y);
      else if (numbers != 2)
          printf("\nBye\n\n");
    }
    while (numbers == 2);
}