Consider the control system which has a root locus plot as given. The open loop transfer function is given by:

Calculation:

In the given figure, there are three poles and one zero in the root locus.

Among all the options, only option 2 consists of three poles and one zero.

Hence, option 2 is correct.

Additional Information G(s)H(s) = $\frac{K(S+3)}{S(S+1)(S+4)}$

The centroid is given by:

${\sigma }_c=\frac{-1-4-(-3)}{2}=-1$

The angle of asymptotes is given by:

$\mathrm{\angle }=\frac{(2k+1)180}{P-Z}$ where, k=0,1 ...(P-Z-1)

$\mathrm{\angle }=\frac{(2\times 0+1)180}{2}=90$ and $\mathrm{\angle }=\frac{(2\times 1+1)180}{2}=270$

The breakaway point is given by:

$\frac{dk}{ds}=0$

$-\frac{d}{ds}(\frac{s(s+1)(s+4)}{(s+3)})=0$

s = -0.51, -3.29 ± j 1.071

s = -0.51 is a valid breakaway point.