Write a C program, named bisection.h, containing the following functions.

1. Function float horner(float *p, int n, float x)
2. Function float bisection(float *p, int n, float a, float b) computes a real root of the polynomial function f(x) = p[0]x^n-1 + p[1]x^n-2 ++ p[n-2]x¹ + p[n-1]x⁰ between interval [a, b] by bisection method when f(a)*f(b) < 0. Use the fault tolerant 1e-6 (or 0.000001) as a stop condition, i.e., if x0 is the actual root and x is a approximate to x0, stop the iteration if |x-x0|<1e-6 or |f(x)| < 1e-6.

Use the provided main program to test the above functions.

Main Program

#include "bisection.h" int main(int argc, char* args[]) { float p[] = {1, 2, 3, 4}; int n = 4; float a = -2, b = 2; float pa = horner(p, n, a); float pb = horner(p, n, b); printf("f(%f): %f ", a, pa); printf("f(%f): %f ", b, pb); if (pa * pb < 0) { float r = bisection(p, n, a, b); printf("root: %f ", r); printf("f(%f): %f ", r, horner(p, n, r)); } return 0; } 

Code so Far: bisection.h

#include #include float horner(float *p, int n, float x); float bisection(float *p, int n, float a, float b); float horner(float *p, int n, float x) { // implementation } //bisection method implementation float bisection(float *p, int n, float a, float b) { // implementation }

public test

 f(-2.000000): -2.000000 f(2.000000): 26.000000 root: -1.650629 f(-1.650629): 0.000001