GATE 2017 EE (EE2) – Question 45

All roots of $s^3+3s^2+2s+K=0$ lie in the open left half-plane for

Show answer and explanation

Correct answer: (A) $0<K<6$

Explanation

The cubic Routh first column is 1,3,(6−K)/3,K. Strict stability requires all four entries to be positive.

Thus K>0 and K<6. Equality at either endpoint puts roots on the imaginary axis, so the interval is open. The required range is **0<K<6, A**.

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