Question

The characteristic equation of a control system is given by s^6+2s^5+8s^4+12s^3+20s^2+16s+16=0 . The number of the roots of the equation which lie on the imaginary axis of s-plane:

(a) 0

(b) 2

(c) 4

(d) 6

The question was posed to me by my school teacher while I was bunking the class.

The doubt is from Stability Analysis in section Digital Control Systems of Control Systems

Answer 1

Correct answer is (c) 4

For explanation I would say: The stability analysis is done using Routh-Hurwitz criterion and hence the number of roots on the right is calculated.