Problem -

Consider the quartic equation

x⁴ + ax³ + bx² + cx - 1 = 0,                                             (1)

where a, b, c, and d are real input coefficients. Develop a matlab program to find all roots of equation (1) using the methods discussed in class. Your program can not use the matlab built-in functions fzero, roots, eig, and eigs.

You should turn in a .m file quarticxxx.m which contains a matlab function of the form

function [rts, info] = quarticxxx(C)

where xxx is your student id, C = (a, b, c, d) is the input vector of coefficients, rts is the vector of roots and info is your output message.

Your program will be stress-tested against typical and pathological quartic equations:

1. equations with random C;

2. equations with very large C; or

3. equations with double roots or nearly double roots; or

You will receive partial credit for each correct root (accurate to within a. relative error of at most 10^-5, as compared to the roots function in matlab) receive additional credit.