Root Locus in a feedback loop
Since you have the closed-loop system you need to put it into the from \$1+\frac{k n(s)}{d(s)}=0\ \$ to use the standard root locus techniques.

The roots depend on only the denominator of the closed-loop system.

$$ s^3+K s^2+7 s^2+7 K s+10 s+20 K =0$$

$$ s^3+7 s^2+10 s+K (s^2+7 s+20) =0$$

$$1+\frac{K (s^2+7 s+20)}{s^3+7 s^2+10 s}=0$$

And from the root locus it can also be seen that is system is stable for \$K&gt;0\$.