What is the centroid of the given root locus?

[magnifik]

i just want to make sure I'm doing this correctly as there is some discrepancy in my textbook. i know the centroid is equal to (Ʃpoles - Ʃzeros) / (# of poles - # of zeros)

the equation i have is s² + 2s + 8 / s(s² + 2s + 10)

so the zeros are -1 + i√7 and -1 - i√7
and the poles are 0, -1 + 3i, -1 - 3i

and the centroid = (0 - 1 - 1) - (-1 -1) / (3-2) = 0

in my textbook they say that the answer is -2.. am i missing something?
my textbook has been wrong before...

 

[DeeJay]

(0-2)/1= -2 The 2nd order pole is complex. The sum of the roots are 0. The zeros should be (-4,2) {not -1-1 as shown} or -4+2=-2. Your denominator calculation is correct that 3poles -2zeros is 1. The correct answer should be -2