How can I prove that for any control system root locus plot starts from poles of OLTF and ends at zeroes of OLTF?
The CLTF is: \$ T(s)=\frac{KN(s)}{D(s)+KN(s)}\$, and the characteristic equation (CE) is:

\$\small D(s)+KN(s)=0\$

As \$\small K\$ goes from zero to infinity, the roots of the CE trace out the root locus, which is the path of the closed loop poles in the complex s-plane.

For the start and end points of the locus, we let \$\small K=0\$ and \$\small K\rightarrow\infty\$, respectively, as follows:

When \$\small K=0\$, the CE is: \$\small D(s)=0\$, and the roots are thus the poles of the open loop TF.

When \$\small K\rightarrow \infty\$, \$\small KD(s)&gt;&gt;N(s)\$, and the CE is: \$\small KN(s)=0\$; hence \$\small N(s)=0\$, and the roots are the zeroes of the open loop TF.