A certain system has transfer function $G(s)=\dfrac{s+8}{s^{2}+\alpha s-4}$, where $\alpha$ is a parameter. Consider the standard negative unity feedback configuration as shown below.
Which of the following statements is true?
- The closed loop system is never stable for any value of $\alpha$.
- For some positive values of $\alpha$, the closed loop system is stable, but not for all positive values.
- For all positive values of $\alpha$, the closed loop system is stable.
- The closed loop system is stable for all values of $\alpha$, both positive and negative.