GATE 2025 IN – Question 27
For $G(s)=1+\dfrac{2s-1}{s^3+5s^2+3s+22}$, the number of zeros in the left half of the $s$-plane is
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Correct answer: (D) 3
Explanation
Combine the constant and fraction: the numerator is s³+5s²+5s+21.
Its Routh first column is 1,5,(25−21)/5=0.8,21, all positive.
Therefore all three numerator roots lie in the left half-plane, giving **3, D**.
No pole–zero cancellation changes this count.