Correct Option: A

Given,

KG(s) =	K(s + a)	; b > a
	s2(s + b)

Here, pole are at s = 0, 0, – b and zero are at s = – a The asymptote angles are

=	(2q + 1)	q = 0, 1.
	p – z

= 90° and 270° degrees.
Centroid is at,

σ =	– (real part of all poles – real parts of all zeros)
	p – z

=	– (b – a)
	3 – 1

=	– b + a
	2

The characteristic equation is, 1 + KG(s) = 0
or

1 +	K(s + a)	= 0
	s2(s + b)

or
s³ + bs² + Ks + Ka = 0
and, Routh array is
s³ 1 K
s² B Ka
s¹ Kb – Ka/b
s⁰ Ka
Since given that, b > a, therefore the system is always stable i.e., there is no intersection on the imaginary axis. Hence the roots locus meets the imaginary axis at s = 0. So, alternative (A) is the correct choice.