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I was calculating the eigenvalues of a matrix and the output contained some eigenvalues like:

Root[148 + 480 x - 144 x^4 + (399 - 4 x + 296 x^2 + x^4) #1 + (-156 - 2 x^2) #1^2 + #1^3 &, 1]
Root[148 + 480 x - 144 x^4 + (399 - 4 x + 296 x^2 + x^4) #1 + (-156 - 2 x^2) #1^2 + #1^3 &, 2]

and

Root[148 + 480 x - 144 x^4 + (399 - 4 x + 296 x^2 + x^4) #1 + (-156 - 2 x^2) #1^2 + #1^3 &, 3]

where $x$ is a variable in my original matrix. I want to further manipulate the eigenvalues, but I simply do not understand what these eigenvalues mean.

M Shehzad
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    Root[fun[..],1] is an exact number, namely a root of f[..]==0. It is the first roor. Root[f[..],2] is the next root. To get an numerical approximation by machine numbers: N[Root[...]] – Daniel Huber Sep 23 '23 at 12:09
  • You can also try ToRadicals on the Roots to get them in terms of radicals if you would like an exact representation that is not a Root object. It is not always possible to express a root in terms of radicals however (it is for your 3 examples though) – ydd Sep 23 '23 at 14:00

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