In order to draw the root locus, you need to convert the open-loop system into the closed-loop system. You can do this

$$
\begin{align}
T(s) &= \frac{   \frac{1}{(s+3)(s+4)}   }{ 1+ \frac{1}{(s+3)(s+4)} \frac{K}{s(s+1)} } \\
&= \frac{s^2+s}{s^4+8s^3+19s^2+12s+K}
\end{align}
$$
Now the gain K appears in the characteristic equation of the closed-loop \$T(s)\$ (i.e the denominator). You can easily vary K from 0 to infinity to compute the poles of the characteristic equation of the closed-loop \$T(s)\$ using any software (e.g. Matlab). If the gain K is zero, we have these poles  0,-1,-3,-4. Use this Matlab script to compute the poles at different gains 

    K=0; % vary it from 0 to big number
    poles = roots([1 8 19 12 K])

You just need tabular data to plot the root locus. You may use Matlab as well. 

    GH=zpk([],[0 -1 -3 -4],1);
    sys=tf(GH);
    rlocus(GH)

[![enter image description here][1]][1]


Let's go back to ` roots([1 8 19 12 K])` if K is 178, we have these poles 

      -4.8276 + 2.3442i
      -4.8276 - 2.3442i
       0.8276 + 2.3442i
       0.8276 - 2.3442i

We can see same result in the root locus obtained by Matlab at this gain, 

[![enter image description here][2]][2]


  [1]: https://i.sstatic.net/aZJxo.png
  [2]: https://i.sstatic.net/fuqQi.png