I have been trying to compute the eigenvalues of the following hessian matrix but have been unable to thus far:
$$ \begin{pmatrix} 2a & c & 0\\ c & 2b & d \\ 0 & d & 2b \\ \end{pmatrix} $$
I have gotten to the stage where:
$ \det(H-\lambda I) = (2a-\lambda )(2b-\lambda )^2 - (2a-\lambda )(d)^2 - (2b-\lambda )(c)^2 $
I can't seem to solve for $ \lambda_i $, is there something that I am missing?