  A pair of symmetric bilinear forms A and B determine a binary form $f(x,y) =
disc(Ax-By)$. We prove that the question of whether a given binary form can be
written in this way as a discriminant form generically satisfies a local-global
principle and deduce from this that most binary forms over $\mathbf{Q}$ are
discriminant forms. This is related to the arithmetic of the hyperelliptic
curve $z^2 = f(x,y)$. Analogous results for non-hyperelliptic curves are also
given.
