The open-loop transfer function is given by:
$$G(s) = K \frac{s+4}{s^2+2s+2}$$
For a unity feedback system, the characteristic equation is $1 + G(s) = 0$.
Substituting $G(s)$:
$$1 + K \frac{s+4}{s^2+2s+2} = 0$$
$$s^2+2s+2 + K(s+4) = 0$$
$$s^2 + (2+K)s + (2+4K) =
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