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Recall that the characteristic polynomial of a 2x2 matrix 
is
but
and 
, so the characteristic polynomial for 
is
We're given that the trace is 15 and determinant is 50, so the characteristic polynomial for the matrix in question is
and the eigenvalues are those
for which the characteristic polynomial evaluates to 0.
but
We're given that the trace is 15 and determinant is 50, so the characteristic polynomial for the matrix in question is
and the eigenvalues are those