Root locus region on real axis

Question

Let the open loop transfer function of a positive feedback closed loop system be K(s−3)/(s^2+3s+2), where K is a non-negative real valued parameter.
Consider the corresponding locus of closed loop poles. Which one of the following statements is TRUE?
a)The region (-∞, -2) lies on the root locus
b)The region (-∞, -1) lies on the root locus
c) The region (-2, -1) lies on the root locus
d) The region (-1, 3) lies on the root locus
I drew the root locus of the transfer function but there are two region on real axis
(-infinity,-2) and (-1,3) . But only one option is correct. What option should I choose?

Suba Thomas · Answer

What you have drawn seems to be for negative feedback.
This is the result for positive feedback.
RootLocusPlot[k (s - 3)/(s^2 + 3 s + 2), {k, 0, 10}, FeedbackType -> "Positive"]

Root locus region on real axis

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