Prof. Ming Gu, 861 Evans, tel: 2-3145 Office Hours: MWF 1:30-3:00PM Email: mgu@math.berkeley.edu http://www.math.berkeley.edu/mgu/MA128AFall2017 Math128A: Numerical Analysis Programming Assignment #1 Due Sept. 27, 2017 Consider the quartic equation x4 + ax3 + bx2 + cx 1 = 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. Email your .m file to your GSI by 11:59PM, Sept. 27, 2017