Suppose that the trace of a 2×2 matrix a is tr(a)=15 and the determinant is det(a)=50. find the eigenvalues of a.

The eigenvalues of are 5 and 10.

The eigenvalues of the 2 x 2 matrix are described by the following characteristic polynomial:

(1)

The roots of the characteristic polynomial are defined by the quadratic formula:

(2)

If we know that and , then the eigenvalues of A are:

The eigenvalues of are 5 and 10.

We kindly invite to check this question on eigenvalues: link