  We analyze the characteristic polynomial associated to an ellipsoid and
another quadric in the context of the contact detection problem. We obtain a
necessary and sufficient condition for an efficient method to detect contact.
This condition is a feature on the size and the shape of the quadrics and can
be checked directly from their parameters. Under this hypothesis, contact can
be noticed by means of discriminants of the characteristic polynomial.
Furthermore, relative positions can be classified through the sign of the
coefficients of this polynomial.
