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?
- $L=2, I=2$, and $R=1$
- $L=3, I=2$, and $R=0$
- $L=1, I=2$, and $R=2$
- $L=0, I=4$, and $R=1$
