Write a C program, polynomial.h, containing the following polynomial operation functions:

1. float horner(float p[], int n, float x), which computes and returns the value of the following (n-1)-th degree polynomial p(x) of coefficients p[0], , p[n-1]. p(x) = p[0]x^n-1 + p[1]x^n-2 ++ p[n-2]x¹ + p[n-1]x⁰

2. void derivative(float p[], int n, float d[]), which computes the derivative of input (n-1)-th degree polynomial by p[], output the derivative of (n-2)-th degree polynomial to array d[]. The derivative of the above polynomial p(x) is as follows. p(x) = (n-1)* p[0]x^n-2+ (n-2)p[1]x^n-3 ++ p[n-2]x⁰

3. float newton(float p[], int n, float x0), which finds an approximate real root x of polynomial p(x) using the Newtons method with start position x0. Use the fault tolerant 1e-6 (or 0.000001) as a stop condition, i.e., if r is the actual root, stop the iteration if |x-r|<1e-6 or |p(x)| < 1e-6.

polynomial_main.c

#include

#include

#include

#include "polynomial.h"

void display_polynomial(float p[], int n, float x)

{

int i;

for (i=0; i

if (p[i] > EPSILON && i !=0)

printf("+");

printf("%.2f*%.2f^%d", p[i], x, n-i-1);

}

}

int main(int argc, char *argv[])

{

int n = 4;

float p[] = {1, 2, 3, 4};

int m = 3;

float x[] = {0,1,10};

// test display and horner functions

int i;

for (i=0; i

printf("p(%.2f)=", x[i]);

display_polynomial(p, n, x[i]);

printf("=");

printf("%.2f ", horner(p, n, x[i]));

}

// test derivative function

float d[n-1];

derivative(p, n, d);

for (i=0; i

printf("d(%.2f)=", x[i]);

display_polynomial(d, n-1, x[i]);

printf("=");

printf("%.2f ", horner(d, n-1, x[i]));

}

// test newton function

float x0=-2;

float root = newton(p, n, x0);

printf("root=%.2f ", root);

printf("p(%.2f)=%.2f ", root, horner(p, n, root));

return 0;

}