An open loop transfer function $$G(s)$$ of system is $$G\left( s \right) = {k \over {s\left( {s + 1} \right)\left( {s + 2} \right)}}$$

For a unity feedback system, the breakaway point of the root loci on the real axis occurs at,

The open loop transfer function $$G(s)$$ of a unity feedback control system is given as, $$G\left( s \right) = {{k\left( {s + {2 \over 3}} \right)} \over {{s^2}\left( {s + 2} \right)}}.\,\,$$ From the root locus, it can be inferred that when $$k$$ tends to positive infinity

The characteristic equation of a closed-loop system is $$s\left( {s + 1} \right)\left( {s + 3} \right) + \,\,k\left( {s + 2} \right) = 0,\,\,k > 0.$$

Which of the following statements is true?

A closed loop system has the characteristic function $$\left( {{s^2} - 4} \right)\left( {s + 1} \right) + K\left( {s - 1} \right) = 0.$$
Its root locus plot against $$K$$ is