GATE EC 2025 Set 1 Q27 — Control Systems

Consider the polynomial $p(s)=s^{5}+7 s^{4}+3 s^{3}-33 s^{2}+2 s-40$. Let $(L, I, R)$ be defined as follows.

$L$ is the number of roots of $p(s)$ with negative real parts.

$I$ is the number of roots of $p(s)$ that are purely imaginary.

$R$ is the number of roots of $p(s)$ with positive real parts.

Which one of the following options is correct?