The feedback control system in Figure is stable

Consider the feedback control system shown in figure.
(a) Find the transfer function of the system and its characteristic equation.

(b) Use the Routh-Hurwitz criterion to determine the range of 'K' for which the system is stable.

Given the $$G\left(s\right)H\left(s\right)=\frac K{s\left(s+1\right)\left(s+3\right)}$$, the point of intersection of the asymptotes of the root loci with the real axis is

The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s) has no pole in the right half of s-plane, the number of roots of the system characteristic equation in the right half of s-plane is