  Let $G=< x,t\mid w>$ be a one-relator group, where $w$ is a word in $x,t$. If
$w$ is a product of conjugates of $x$ then, associated with $w$, there is a
polynomial $A_w(X)$ over the integers, which in the case when $G$ is a knot
group, is the Alexander polynomial of the knot. We prove, subject to certain
restrictions on $w$, that if all roots of $A_w(X)$ are real and positive then
$G$ is bi-orderable, and that if $G$ is bi-orderable then at least one root is
real and positive. This sheds light on the bi-orderability of certain knot
groups and on a question of Clay and Rolfsen. One of the results relies on an
extension of work of G. Baumslag on adjunction of roots to groups, and this may
have independent interest.
