The loop transfer function of a single-loop negative feedback system is
L(s) = Gc(s)G{s) = K(s + 2.5)(.5 + 3.2) / s^2(s + 1)(s + 10)(s+ 30)
This system is called conditionally stable because it is stable only for a range of the gain R such that k1 < K < k2. Using the Routh-Hurwitz criteria and the root locus method, determine the range of the gain for which the system is stable. Sketch the root locus for 0 < K < ∞.