Can anyone help with this Matlab Problem please?

Consider the quartic equation

x⁴+ax³+bx²+cx1=0, (1)

where a, b, and c 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] = quarticxxx(C)

where xxx is your student id, C = (a, b, c) is the input vector of coefficients, and rts is the vector of roots;

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

1. (40 points) equations with random C; 2. (30 points) equations with very large C; or 3. (30 points) 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 105, as compared to the roots function in matlab) receive additional credit.

Your program will receive 0 points if the strings fzero, roots or eig (all lower case) show up anywhere in your .m file.