Incomplete source for a program that computes a root of a polynomial of any size with a guessing-based approach

approximate-root.c

// Incomplete source for a program that computes a root of a polynomial of any size with a guessing-based approach
//
// File:         approximate-root
// Compilation:  gcc -o main approximate-root.c
// Run:          ./main

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

double get_value_of_n_degree_polynomial(double x, double *coeficients, int coeficients_length) {
    if (coeficients_length <= 0) {
        return 0;
    }
    if (coeficients_length == 1) {
        return coeficients[0];
    }
    return x*get_value_of_n_degree_polynomial(x, coeficients, coeficients_length-1)+coeficients[coeficients_length-1];
}

int find_root_n_degree_polynomial(double *coeficients, int coeficients_length, double starting_value, double * x_out) {
    double x, last_x, step, target, value, error, next_value, next_error;
    int limit = 100;
    step = starting_value/4;
    last_x = x - step;
    do {
        x = starting_value;

        target = 0;
        value = get_value_of_n_degree_polynomial(last_x, coeficients, coeficients_length);
        error = target - value;

        next_value = get_value_of_n_degree_polynomial(x, coeficients, coeficients_length);
        next_error = target - next_value;

        if (next_error > error) {
            step = - step / 2;
        } else if (next_error < error) {
            step = step * 0.95;
        }
        x = x + step;
    } while (limit-- > 0)
}

int main()
{
    double c[16], x;
    x = 0;
    c[0] = 1;
    c[1] = 7;
    c[2] = 0.5;

    double result;
    result = x*(x*(c[0])+c[1])+c[2];
    printf("Value should be %.3f!\n", result);
    result = get_value_of_n_degree_polynomial(x, c, 3);
    printf("Value is %.3f!\n", result);
    return 0;
}