PROBLEM 5 [2 point] Consider the generic 4-th order polynomial 10(2) =a+bz+022 +d23+z4 with a, b, c, d and d, all real numbers. According to the fundamental theorem of algebra it has 4 roots, i.e. there are 4 values of z for which w(z) = 0; but some or all can coincide. The purpose of this problem is to play with the 4 parameters and see how the roots move through the complex plane as function of the parameters; how they merge, cross or do whatever they need to do. Note that for a = b = c = d = 0 all 4 roots coincide at z = 0. Derive algebraically on paper&pencil how the roots move as function of a when 10(2) 2 a + z4; for negative values of a and also for positive values of (1. Check your answers in Mathematica. Make a plot on paper of the complex plane and mark the location of the roots for a = 1 and for a = 1. Find the roots of 10(2) 2 1 +cz2 +24; for c 0. Do this on paper, by changing variables, 1) = Z2 and using the familiar formula for the roots of quadratic equations. Check your answers in Mathematica. Make a plot on paper of the complex plane and mark their location for c = l and for c = 1. Find the roots for w(z) = 1 + z + 22 + 23 + 24, using Mathematica. Make a plot on paper of the complex plane and mark all roots. Find the roots for w(z) = 1 z + z2 23 + 24, using Mathematica. Make a plot on paper of the complex plane and mark all roots