m For K <0: In this case, using the angle criteria, we can see that the real line segment (5, oo)belongs to the locus since both poles contributes 0 or even integer multiple of T Also, the real line segment(oo, -3)belongs to the locus since both poles contribute T or odd integer multiple of T; the net phase of G(sn) is even integer multiple of T Thus, the root loci containing both K>0(solid line) and K <0(dashed line)cases are shown below (c)Given G(s) has a double-pole at 0 and one finite zero at-1 0: With the angle criteria, we can see that the real line segment (oo,-1 belongs to the locus. Since both poles of G(s) do not belong to the segment, there will be a double-pole point in the segment. To find where it is, use the same technique as in(b)1 × × 1 ≤m ↓e × −3 × 5 • For K < 0 : In this case, using the angle criteria, we can see that the real line segment (5,∗) belongs to the locus since both poles contributes 0 or even integer multiple of �. Also, the real line segment (−∗, −3) belongs to the locus since both poles contribute � or odd integer multiple of �; the net phase of G(sl) is even integer multiple of �. Thus, the root loci containing both K > 0 (solid line) and K < 0 (dashed line) cases are shown below: ≤m −3 5 ↓e (c) Given: s + 1 G(s) = 2 . s G(s) has a double-pole at 0 and one finite zero at −1. • For K > 0 : With the angle criteria, we can see that the real line segment (−∗, −1) belongs to the locus. Since both poles of G(s) do not belong to the segment, there will be a double-pole point in the segment. To find where it is, use the same technique as in (b), 4