GATE EC 2026 Set 1 Q30 — Control Systems

For the control system shown in the Figure, the transfer function of a plant, $G(s)=\frac{1}{(s+1)(s+2)}$ is connected in cascade with a compensator $C(s)=K(s+\alpha)$, where $K$ and $\alpha$ are positive real valued constants.

Which of the following pairs $(K, \alpha)$ represent the correct values for the closed loop system to have poles at $(-3 \pm j \sqrt{5})?$