I need to find the eigenvalues of the linear transformation that the following matrix represent:

$\displaystyle A=\begin{bmatrix}0 & 1 & 0\\ 0 & 0 & 1\\ 4 & -17 & 8\end{bmatrix}$

so I calculated the characteristic polynomial of A:

$\displaystyle f_A(\lambda)=det(\lambda I-A)=\lambda \begin{vmatrix}\lambda & 1\\ -17 & \lambda-8\end{vmatrix}-1\begin{vmatrix}0 & \lambda -8\\ 4 & 1\end{vmatrix}+0\begin{vmatrix}0 & \lambda\\ 4 & -17 \end{vmatrix}$

$\displaystyle f_A(\lambda)=\lambda(\lambda(\lambda-8)+17)-1(-4)$

$\displaystyle f_A(\lambda)=\lambda^3-8\lambda^2+17\lambda+4$

but I have no idea how to find its roots...

any ideas would be greatly appreciated.

TIA!

**edit

Is there another way to find the eigenvalues of A?