Polynomial Matrix Eigenvalue problem. Conditions under which there are only two complex eigenvalues?

Question

I'm solving the polynomial matrix eigenvalue problem $(A\lambda^2+B\lambda+C)v=0 $. This is what I want the eigenvalues to look like. Are there any conditions on the matrices A,B,C such that there are only two complex eigenvalues that are complex conjugates of each other and the rest are purely real. I know the matrices have to be real.