Question

The breakaway point of the root locus on the real axis for a closed loop system with a loop gain \( G(s) = \frac{K(s+10)}{(s+2)(s+5)} \) is:

• A. between -2 and origin
• B. between -2 and -5
• C. between -10 and \( -\infty \)
• D. at \( -\infty \)

Hint:

Breakaway points occur between two real poles or zeros where root locus exists.

Answer 1

The Correct Option is B

The root locus exists on real axis to the left of odd number of poles and zeros. Poles are at -2 and -5. So, root locus lies between -2 and -5 on the real axis, and the breakaway point lies in this interval.