Confused about applying Routh Hurwitz to $s^2 +s + k$
Second order Routh Hurwitz:

$$a_0s^2+a_1s+a_2 = 0$$

$$\begin{cases}
s^2 &amp; a_0 &amp; a_2\\
s^1 &amp; a_1 &amp; 0\\
s^0 &amp; a_2\\
\end{cases}$$

In your example

$$\begin{cases}
s^2 &amp; 1 &amp; k\\
s^1 &amp; 1 &amp; 0\\
s^0 &amp; k\\
\end{cases}$$

Hence, $k$ should be positive.