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 _____________

For the system shown in the figure, s = –2.75 lies on the root locus if K 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 __________________.

The characteristic equation of a unity negative feedback system 1 + KG(s) = 0. The open loop transfer function G(s) has one pole at 0 and two poles at -1. The root locus of the system for varying K is shown in the figure.

The constant damping ratio line, for $$\xi$$ = 0.5 , intersects the root locus at point A. The distance from the origin to point A is given as 0.5. The value of K at point A is ________ .