If P is the number of open-loop poles and Z is the number of open-loop zeros, what is the number of root locus branches when P=Z ?

Correct option is A

​$$\text{In root locus theory:} \\[8pt]\bullet \ \text{The number of root locus branches equals the number of open-loop poles } (P). \\[4pt]\bullet \ \text{Each branch starts at an open-loop pole and ends at an open-loop zero.} \\[6pt]\bullet \ \text{If the number of poles and zeros are equal } (P = Z), \text{ then:} \\[4pt]\quad \bullet \ \text{There are no excess poles.} \\[2pt]\quad \bullet \ \text{Hence, no branches go to infinity.} \\[10pt]\text{Therefore, all root locus branches originate from finite open-loop poles and terminate at finite open-loop zeros.}$$​​