Implement the Newton-Raphson method in a programming language, i.e., define someting like the following Python function:

def Newton_solve(f, fp, x0, tol=0.001, maxiter=100):
    """
    Find a zero of the function f using the Newton-Raphson Method 
    starting in x0, with tolerance tol (default: 0.001), and 
    maximum number of iterations equal to maxiter (default: 100).
    fp denotes the derivate of f
    """

Make sure that your function returns the number of iterations required in addition to the approximation found.

1. Apply the function Newton_solve to the polynomial \(x^2-x-1\) with starting value \(1.0\) to approximate the golden ratio \(\tfrac{1}{2}\!(1+\sqrt{5})\approx 1.61803398875\) in 9 significant digits. How many iterations do you need?
   
   
2. Apply the function Newton_solve to polynomial \(x^3+x^2-2\) with starting value \(1.5\).
   After how many steps did you determine the zero point \(1\) in 10 significant digits?
   Explain what happens when you choose \(-1.5\) as your starting value.
   
   
3. Apply function Newton_solve to polynomial \(x^3-3x^2+2\) with starting value \(1.77\).
   After how many steps did you determine the zero point \(1\) in 10 significant digits?
   What happens when you choose \(1.78\) as your starting value?