Consider the cubic equation
ax3 + bx2 + cx + d = 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 appropriate methods. Your program can not use the matlab built-in functions fzero and roots.
You should turn in a .m file cubicxxx.m which contains a matlab function of the form function [rts,info] = cubicxxx(a,b,c,d)
where xxx is your student id, rts is the vector of roots and info is your output message. Your program will be stress-tested against cubic equations that may have
1. random roots; or
2. very large or very small roots; or
3. multiple roots or nearly multiple roots; or
4. less than 3 roots or more than 3 roots.
You will receive credit for a test polynomial only if your program gets the number of roots
correctly, and only then will each correct root (accurate to within a relative error of at most 10^-16,
as compared to the roots function in matlab) receive additional credit.
Your program will receive 0 points if the strings fzero or roots (both in lower case letters)
show up anywhere in your .m file.