  In this paper we propose a sequence of tests which gives a definitive test
for checking $2\times M$ separability. The test is definitive in the sense that
each test corresponds to checking membership in a cone, and that the closure of
the union of all these cones consists exactly of {\it all} $2 \times M$
separable states. Membership in each single cone may be checked via
semidefinite programming, and is thus a tractable problem. This sequential test
comes about by considering the dual problem, the characterization of all
positive maps acting ${\mathbb C}^{2 \times 2} \to {\mathbb C}^{M\times M}$.
The latter in turn is solved by characterizing all positive quadratic matrix
polynomials in a complex variable.
