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I was trying to find eigenvalues of a matrix. I calculated the characteristic polynomial by calculating (A-lambdaI) and then calculating it's determinant. The results was:

[tex]-\lambda ^{3}+8\lambda ^{2}-20\lambda +16[/tex]

which is the correct calculation.

Now, the eigenvalues are 2,2,4, but I do not know, technically, how am I suppose to find it from:

[tex]-\lambda ^{3}+8\lambda ^{2}-20\lambda +16 = 0[/tex]

I mean, how do I expand this polynomial into:

[tex](\lambda -4)(\lambda -2)^{2}[/tex]

assuming that I do not see it in my eyes immediately, is there some hint to look for ?

Just to supply all information, the matrix is:

[tex]\begin{pmatrix} 3 &2 &3 \\ -1 &0 &-3 \\ 1 &2 &5 \end{pmatrix}[/tex]

thanks !!