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Well, Im not sure if this is true for all matrices of all sizes, but for a 2x2 square matrix the discriminant is...
dis(A) = tr(A)^2 - 4 det(A)
The discriminant of matrix A is equal to the square of the trace of matrix A, minus four times the determinant of matrix A.
I know this to be true for all 2x2 square matrice, but I have never seen any statement one way or the other for larger matrices.
Thus, for matrix A = [ a, b; c, d ]
tr(A) = a+d
det(A) = ad-bc
tr(A)^2 = a^2 + 2ad + d^2
4 det(A) = 4ad - 4bc
dis(A) = a^2 - 2ad + 4bc + d^2
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