A linear time invariant (LTI) system with the transfer function $$$G\left(s\right)=\frac{K\left(s^2+2s+2\right)}{s^2-3s+2}$$$ is connected in unity feedback configuration as shown in the figure.

For the closed loop system shown, the root locus for 0 < K < $$\infty$$ intersects the imaginary axis for K = 1.5. The closed loop system is stable for

The open-loop transfer function of a unity-feedback control system is $$$G\left(s\right)=\frac K{s^2+5s+5}$$$ The value of K at the breakaway point of the feedback control system's root-locus plot is _____________

The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $$G\left(s\right)=\frac{K\left(s+2\right)}{s^2+2s+2}$$ and H(s) = 1 respectively.If the variable parameter K is real positive, then the location of the breakaway point on the root locus diagram of the system is_____________.

The open-loop transfer function of a plant in a unity feedback configuration is given as $$G\left(s\right)=\frac{K\left(s+4\right)}{\left(s+8\right)\left(s^2-9\right)}$$.The value of the gain K(>0) for which -1 + j2 lies on the root locus is __________________.