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Consider a negative unity feedback system with the forward path transfer function

$\large\frac{s^{2}+s+1}{s^{3}+2s^{2}+2s+K},$ where $\text{K}$ is a positive real number. The value of $\text{K}$ for which the

system will have some of its poles on the imaginary axis is ____________.

  1. $9$
  2. $8$
  3. $7$
  4. $6$
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