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 methods discussed in class. Your program can not use the matlab built-in functions fzero and roots.

Your program will be stress-tested against cubic equations that may have 1. (40 points) random roots; or 2. (20 points) very large or very small roots; or 3. (20 points) multiple roots or nearly multiple roots; or 4. (20 points) less than 3 roots or more than 3 roots