In system modelling using transfer function, roots of the characteristic equation are 

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  1. Zeros of the transfer function
  2. Poles of the transfer function
  3. It can be poles or zeros depending on the stability of the system
  4. It is neither pole nor zero

Answer (Detailed Solution Below)

Option 2 : Poles of the transfer function
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Explanation:

In system modeling using a transfer function, the roots of the characteristic equation are the Poles of the transfer function.

  • The characteristic equation of a system is typically obtained by setting the denominator polynomial of the closed-loop transfer function to zero.
  • The poles of a transfer function are the values of 's' that make the denominator of the transfer function equal to zero (assuming no common factors with the numerator).
  • The locations of the poles in the s-plane are critical for determining the stability and transient response of a system. If any pole lies in the right half of the s-plane, the system is unstable.
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