A transfer function is given below Find its poles and zeros

A transfer function is given below. Find its poles and zeros and determine whether it is the TF of a stable system. H(s)=2s^2 +12s16 / 2s^2+24s+8

A)Zeros at7.1231,+1.1231, poles at 11.6569, 0.3431, stable

B)Zeros at7.1231,1.1231, poles at 11.6569, 0.3431, stable

C)Zeros at+7.1231,+1.1231, poles at+11.6569, 0.3431, unstable

D)Zeros at6,+8, poles at 12, 4, stable

Solution

Option d

On solving quadratic equation of h(s) we get numerator roots are zeros and denominator roots are poles.

For stability by using R-H criteria as there is no sign changes in the characteristic equation the give transfer function is stable

Zeros at -6 ,+8,poles at -12,-4,stable.