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GATE 2018 EE – Question 44

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Multiple choice

The number of roots of the polynomial, $s^7+s^6+7s^5+14s^4+31s^3+73s^2+25s+200$, in the open left half of the complex plane is

  1. 3
  2. 4
  3. 5
  4. 6

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Show answer and explanation

Correct answer: (A) 3

Explanation

Applying the Routh-Hurwitz test to the polynomial gives several sign changes in the first column, so some of its seven roots are in the right half plane. According to the official key, 3 of the roots lie in the open left half plane.