The closed loop transfer function of a single-loop negative feedback system is:

G_{c}(s)G(s) = K(s+2)(s+3) / s²(s+1)(s+10)(s+50)}

This system is called conditionally stable because it is stable only for a range of the gain K 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