Correct Option: D

Given G(s) H(s) =	K(s + 6)
	(s + 3)(s + 6)

the pole-zero plot of the given function is shown below C. E. is given by
1 + G(s) H(s) = 0

1 +	K(s + 6)	= 0
	(s + 3)(s + 5)

or

K = –	(s + 3) (s + 5)	= 0
	(s + 6)

or	dK	= -		(s + 6) d/ds (s2 + 8s + 15) – (s2 + 8s + 15) d/ds (s + 6)
	ds			(s + 6)2

= -		(s + 6) (2s + 8) – (s2 + 8s + 15)1
		(s + 6)2

= –		2s2 + 208 + 48 – s2 – 8s – 15
		(s + 6)2

or

dK	= –		s2 + 12s + 33
ds			(s + 6)2

dK/ds = 0 gives
s² + 12s + 33 = 0
on solving we get

s =		– 12 ± √10
		2

= – 7.58, – 4.42
Note: Since break away point lies between two poles and the break in point lies between two zeros. Since here one zero at s = – 6 and other at infinity. Hence only option (D) is the correct choice not option (C).