So I have the following transfer function
$$G(s)=\frac{s^2+0.1s}{10s^3 + 1.1s^2 + 0.01s + 2K}$$
Now I'm trying to determine the value of K so that I have a marginally stable system. I'm not supposed to use the Routh-Hurwitz method. I'm thinking hard but I seem to get to nowhere. I know that for the system to be marginally stable I will need a real pole in the left complex plane and two complex conjugate pure imaginary poles. But how can I determine the exact value of K that will provide me with those 3 specific poles?