Figure shows a feedback system where K

Figure shows a feedback system where K > 0. The range of K for which the system is stable will be given by

K > 0
Characteristic equation of the system is
1 + G(s) H(s) = 0

⇒ 1 +	K	= 0
	s(s + 3)(s + 10)

⇒ s(s² + 13s + 30) + K = 0
⇒ s³ + 13s² + 30s + K = 0
Routh array

For system to be stable, all element of first column must be positive.

∴	390 - K	> 0
	13

⇒ K < 390°
and K > 0
Hence range of K is 0 < K < 390