For all problems, apply and clearly indicate the root-locus rules, derive all relevant expressions etc. For finding roots of polynomials, you can use Matlab (or some other numerical SW). Hint: If necessary, for finding angles, use trigonometry - by knowing the coordinates/distances between points, you can find angles using arcsin, arccos, arctan - especially easy for coordinates forming right-angle and/or isosceles triangles. Providing just a picture of the root locus without explanations/derivation will bring 0 points. A problem like this WILL be in the final exam. For practice -sketch root locus without using MATLAB. (You can use Matlab function "rlocus" to check the result). For all problems - given a transfer function L(s) and assuming the root-locus satisfies the equation 1+KL(s)=0, where K>O is a real parameter, derive all relevant parameters: breakaway/break-in points centroid, asymptote angles, angles of departure/arrival from complex conjugate poles/zeros whether the system can become unstable - intersection with the Imaginary axis, the value of K for which the system becomes unstable draw the root-locus of the system. Problem 1 L(s) = (s+2)(2+4) What kind of open-loop system is this in terms of stability (comment on the location of original poles)? What are the locations of closed loop poles (in unity feedback) when K=10 ? Has this particular system become more or less stable when you apply (more) gain