  We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary
terms. By exploiting certain functional relations at roots of unity, we derive
a generalized form of T-Q relation involving more than one independent Q(u),
which we use to propose the Bethe-ansatz-type expressions for the eigenvalues
of the transfer matrix. At most two of the boundary parameters are set to be
arbitrary and the bulk anisotropy parameter has values \eta = i\pi/2,
i\pi/4,... We also provide numerical evidence for the completeness of the
Bethe-ansatz-type solutions derived, using s = 1 case as an example.
