[5pt, extra credit] In this problem, you will write a code that will find all of the roots of the function $f(x) = x^5 - 3x^2 + 1$ inside the interval [-2, 2]. For each part, please submit a print-out of your code along with the values you obtain for the roots.
(a) Using the fact that the roots of $f$ on this interval are separated by at least 0.25, write a program that implements the bisection algorithm to obtain estimates of the roots that are accurate to within 0.1.
(b) Using the estimates of the roots obtained in the previous part, write a program that implements Newton's method to refine the values of the roots such that the difference between successive iterates is at most $10^{-12}$.
