The open loop transfer function of a closed loop control system is given as: \(G\left( s \right) = \frac{{K\left( {s + 2} \right)}}{{s\left( {s + 1} \right){{\left( {s + 4} \right)}^2}}}\).

What are the number of asymptotes and the centroid of the asymptotes of the root-loci of closed loop system?

1
\( - 3;\;\;\left( {\frac{7}{3},\;0} \right)\)
2
-2; (2, 0)
3
\(3;\left( {\frac{{ - 7}}{3},\;0} \right)\)
4
2; (-2, 0)

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