List of top Control Systems Questions on Root Locus and Compensator Design - Pole Placement asked in GATE EC

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. The compensator and plant are placed in the forward path of a unity negative feedback system with input \(R(s)\) and output \(Y(s)\).
Which of the following pairs \((K,\alpha)\) represent the correct values for the closed loop system to have poles at \(\left(-3\pm j\sqrt{5}\right)\)?