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If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s^2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be

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If a feedback control system has its open loop transfer function G(s)H(s) = K/(s-2)(s^2+3s+5) has the root locus plot which intersects the imaginary axis at s =0, then the value of K at this point will be

(a) -5

(b) 10

(c) 5

(d) -10

I have been asked this question in homework.

My question comes from Construction of Root Loci in division The Root Locus Technique of Control Systems

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The correct choice is (b) 10

Easiest explanation: The intersection point on the imaginary axis at s =0 is obtained by Routh Hurwitz criteria making s^0 row zero and getting the value K = 10.

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