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First of all find the closed loop transfer function of the system

I meant \[\frac{Y}{X}=...\]

You'd need to find the poles of the system, sorry I was dealing in the s- domain

Poles are at \[\frac{k\pm\sqrt{k^2-4b}}{2}\]

Let me know if you have doubt anywhere

so you undestood now ?

No.

oops, did you ask this doubt to your teacher?

*in the lecture notes

umm, where did calculus was used?

He has NEVER used calculus in this course.

p = pole
p = 1 => remains (unchanged)
|p| >1 => diverge
|p| < 1 => converge

now you need to check which one lies in, out or on the unit circle. then you can classify the system

???

I think I understand how to analyze the system now, thanks :)

welcome :P