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eigenvalues of matrices or operators

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Eigenvalues of symmetric tridiagonal matrices with identical off diagonal elements

Is there a simple analytical solution to obtain eigenvalues (and eigenvectors) for this type of tridiagonal matrices ? … identical and the matrix is symmetric) $$ \begin{pmatrix} a_{1}-k & k & 0 & 0 \\\ k & a_{2}-2\cdot k & k & 0 \\\ 0 & k & -a_{2}-2\cdot k & k \\\ 0 & 0 & k & -a_{1}-k \end{pmatrix} $$ To obtain eigenvalues
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