Write a program that implements the bisection method for root finding. Your program should be similar to the Etter & Ingber Chapter 6_9 program on blackboard since it is a variation on the same technique. Your program should find the roots to some user defined tolerance.

Here is the code:

/*----------------------------------------------------*/ /* Program chapter6_9 */ /* */ /* This program estimates the real roots of a */ /* polynomial function using incremental search. */ #include //Required for cin, cout #include //Required for cell() using namespace std; // Function Prototypes void check_roots(double left, double right, double a0, double a1, double a2, double a3); double poly(double x, double a0, double a1, double a2, double a3); int main() { // Declare objects and function prototypes. int n; double a0, a1, a2, a3, a, b, step, left, right; // Get user input. cout > a0 >> a1 >> a2 >> a3; cout > a >> b; cout > step; //Check subintervals for roots. n = ceil((b - a)/step); for (int k=0; k

Use your programs for the following physics problem:

Modern Physics: The black body radiation curve has a peak that can be determined by maximizing the Planck radiation formula in frequency form with respect to frequency. The Planck radiation formula is

If we take the derivative of the equation above and set it equal to zero and then substitute x = (hn/kT) we get an expression that reduces to

Solve for the roots of this equation to determine the constant for Wiens law. Use the bisection method and the Newton Raphson method. You will need to replace the function in each program with equation 1 above.

From your value of x determine the constant in Wiens law:

Add a few lines of code to each program to (a) calculate the value of the constant and (b) compare your results to the standard constant (i.e. take a % error) from a your textbook.

(e -1)