Find any root with this algorithm!

root.c

#include <stdio.h>
#include <stdlib.h>

#define ROOT        1.21
#define POTENCY     2
#define PHASES      60
#define PRECISION   15

double* find_root(double *, double, int, int);
double  potency_by(double, int);

int main(void) {
    double range[] = {0.0, 0.0};

    double* values = find_root(range, ROOT, POTENCY, PHASES);

    printf("[%.*f ;; %.*f]\n", (int)PRECISION, (double)*(values + 0)\
                             , (int)PRECISION, (double)*(values + 1));

    return 0;
}

double* find_root(double list_range[], double root, int potency, int phases) {

    if(root <= 0.0 || root == 1.0)
        return 0;

    double x = 0.0;
    double r = 0.0;

    list_range[1] = root;

    for(; phases >= 0; phases--) {
        x = (list_range[0] + list_range[1]) / 2;

        r = potency_by(x, potency);

        if((r) > root)
            list_range[1] = x;
        else if((r) < root)
            list_range[0] = x;
        else {
            printf("Root: %f\n", x);
            exit(0);
        }
    }

    return list_range;
}

double potency_by(double base, int potency) {
    double result = 1.0;

    for(; potency > 0; potency--)
        result *= base;

    return result;
}