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...

Consider the cubic equationax3 + bx2 + cx + d = 0, (1)where a, b, c, and d are real input coefficients. Develop a matlab program to find all roots ofequation (1) using the appropriate methods. Your program can not use the matlab built-infunctions fzero and roots.You should turn in a .m file cubicxxx.m which contains a matlab function of the formfunction [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 have1. random roots; or2. very large or very small roots; or3. multiple roots or nearly multiple roots; or4. 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 rootscorrectly, 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.

function [rts,info]=cubic125(a,b,c,d)Q=(b^2-3*c*a)/(9*a^2);R=2*b^3/(27*a^3)-b*c/(6*a^2)+d/(2*a);R2=R^2;Q3=Q^3;if (R2<Q3) %Three real rootsthita=acos(R/sqrt(Q3));SQ=sqrt(Q);...