You need the program to find all the roots of a quartic

Question

Can you please write a matlab code for finding all roots in a quartic equation using Newton's Method

You need the program to find all the roots of a quartic equation (i.e. x⁴ + ax³ + bx² + cx - 1 = 0) without using built-in functions fzero, roots, eig, and eigs.

The program will be stress-tested against typical and pathological quartic equations, such as equations with a random C, equations with a very large C, and equations with double roots or nearly double roots.