where

\(A = [\frac{a b}{c d}]\) (ignore the line, it is a matrix but don't know how to do it in LaTex so used the fraction function)

So my characteristic equation is:

\(\lambda^2 -tr(A)\lambda + det(A) = 0\)

where \(tr(A) = a + d\) and \( det(A) = ad - bc\)

How would I solve the eigenvalues for the above function? I understand that it is the values of \(\lambda = 0\) but not sure how to make the function to to zero in this general case... Thanks!