Trying to find eigenvalues for this matrix

If my math is correct, the determinant of this is , but this doesn't factor, so I don't know how to find the roots.

Can somebody help? Thanks.

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- Dec 4th 2012, 08:45 PMjoatmonEigenvalues for 3x3 Matrix
Trying to find eigenvalues for this matrix

If my math is correct, the determinant of this is , but this doesn't factor, so I don't know how to find the roots.

Can somebody help? Thanks. - Dec 4th 2012, 10:47 PMDevenoRe: Eigenvalues for 3x3 Matrix
your math is incorrect.

the determinant is:

(1 - λ)^{3}- (-2)(-2)(1 - λ) - (2)(2)(1 - λ) = 1 - 3λ + 3λ^{2}- λ^{3}- 8(1 - λ) = -7 +5λ + 3λ^{2}- λ^{3}

this has one rational root, and two irrational roots which are "conjugate" (in the sense of square roots).