a$.$ What Root Locus plot is used for in control problems?

Consider a unity feedback system with the loop transfer function

$G(s)=\frac{K(s+10)(s+20)}{(s+30)(s^2-20s+200)}$

Draw the system root locus RL sketch. Specify the following:

b$.$ How many RL branches or sections the sketch has?

c$.$ How many RL branches end at infinity?. $q,$

d$.$ What are the asymptotes centroid and angles? $q,$

e$.$ Where the breakaway occurs?. $q,$

f$.$ What are the departure and arrival angles?.. $q,$

g$.$ Where the imaginary axis crossings occur? $q,$

h$.$ What range of K would give you real poles only?... $q,$