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Root locus of s(s+2)+K(s+4) =0 is a circle. What are the coordinates of the center of this circle?

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Root locus of s(s+2)+K(s+4) =0 is a circle. What are the coordinates of the center of this circle?

(a) -2,0

(b) -3,0

(c) -4,0

(d) -5,0

I have been asked this question in an online interview.

My doubt stems from The Root Locus Concepts topic in division The Root Locus Technique of Control Systems

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The correct answer is (c) -4,0

For explanation I would say: s(s+2)+K(s+4) =0

1+K(s+4)/s(s+2) =0.

G(s)H(s) =K(s+b)/s(s+a)

Centre =(-b,0) =(-4,0).

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