Determine the value of a constant for which the system is marginally stable
I guess the simplest way of making sure the roots are located correctly is:

A polynomial with one real root and 2 imaginary roots generally looks as follows:

$$
A\cdot (s+a)\cdot (s^2 + b)
$$

This needs to match the denominator, so

$$\begin{align}
10\cdot (s + a)\cdot (s^2 + b) &amp;= 10\cdot s^3 + (10a) \cdot s^2 + (10b)\cdot s + (10\cdot a\cdot b) \\
&amp;= 10\cdot s^3 + 1.1 \cdot s^2 + 0.01\cdot s + 2K
\end{align}$$

From this it immediately follows that

$$\begin{align}
a &amp;= \frac{1.1}{10} = 0.11\\
b &amp;= \frac{0.01}{10} = 0.001\\
K &amp;= \frac{10\cdot a\cdot b}{2} = \frac{0.11\cdot 0.001}{2} = 55\cdot 10^{-5}
\end{align}$$