Find the eigenvalues of
$$
\left(\begin{matrix}
C\_1 & C\_1 & C\_1&\cdots&C\_1 \\
C\_2 & C\_2 & C\_2&\cdots &C\_2 \\
C\_3 & C\_3 & C\_3&\cdots&C\_3 \\
\vdots&\ & \ & \ & \vdots\\
C\_n & C\_n & C\_n&\cdots&C\_n \\
\end{matrix}\right)
$$

My approach:
$$\left|
\begin{matrix}
C\_1-λ & C\_1 & C\_1&...&C\_1 \\
C\_2 & C\_2-λ & C\_2&...&C\_2 \\
C\_3 & C\_3 & C\_3-λ&...&C\_3 \\
\vdots & \ & \ & \ & \vdots\\
C\_n & C\_n & C\_n&...&C\_n-λ
\end{matrix}\right|
$$
and i eventually have 
\begin{align}
\ -λ^3 +(C\_1+C\_2+C\_3)λ^2-C\_1C\_3λ-C\_1C\_2=0
\end{align} 

and then I'm lost at this stage...