  We give a separation bound for the complex roots of a trinomial $f \in
\mathbb{Z}[X]$. The logarithm of the inverse of our separation bound is
polynomial in the size of the sparse encoding of $f$; in particular, it is
polynomial in $\log (\deg f)$. It is known that no such bound is possible for
4-nomials (polynomials with 4 monomials). For trinomials, the classical results
(which are based on the degree of $f$ rather than the number of monomials) give
separation bounds that are exponentially worse.As an algorithmic application,
we show that the number of real roots of a trinomial $f$ can be computed in
time polynomial in the size of the sparse encoding of~$f$. The same problem is
open for 4-nomials.
