using python

Problem 4. Determine all of the roots of the polynomial f(x) = x3 25x2 + 165x 275 using the combined Bisection/Newton-Raphson iteration given in the notes. Write a single function which the returns both the value of the polynomial f(x) and its derivative f'(x), and pass it as an argument to your newton root-finding function. Make your function check its inputs (i.e. check that the root is really bracketed by the input bounds) and do any other bomb-proofing" you can think of. Again, make a plot of the function first to get a feel for the shape of the curve to determine a good initial guess for the root. (Different values of the initial guess will of course cause the iteration to converge to different roots.) Have the code which calls your root-finding function demonstrate that the result re- turned is in fact correct within the given tolerance. As a check, insert the roots you find back into the function and see how close these results are to zero