Let A(n) and B(n) be sequences of $m imes m$ random matrices with a joint asymptotic distribution as $n o infty$. The asymptotic distribution of the ordered roots of $$mid$A(n) - f B(n)$mid$ = 0$</TEX> depends on the multiplicity of the roots of a determinatal equation involving parameter roots. This paper treats the asymptotic distribution of the roots of the above determinantal equation in the case where some of parameter roots are zero. Furthermore, we apply our results to deriving the asymptotic distributions of the eigenvalues of the MANOVA matrix in the noncentral case when the underlying distribution is not multivariate normal and some parameter roots are zero.