GATE 2016 EE – Question 43
Given the following polynomial equation
$$s^3 + 5.5 s^2 + 8.5 s + 3 = 0,$$
the number of roots of the polynomial, which have real parts strictly less than $-1$, is ________.
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Correct answer: 2
Explanation
Shift the variable by writing $s = z - 1$. A root with real part less than $-1$ in $s$ is a root with negative real part in $z$. Substituting gives $z^3 + 2.5z^2 + 0.5z - 1 = 0$. The Routh array first column is 1, 2.5, 0.9, $-1$, which has exactly one sign change, so one root has positive real part and the other two have negative real parts. The answer is 2.