  Let $x_1,...,x_{n}$ be real numbers, $P(x)=p_n(x-x_1)...(x-x_n)$, and $Q(x)$
be a polynomial of degree less than or equal to $n$. Denote by $\Delta(Q)$ the
matrix of generalized divided differences of $Q(x)$ with nodes $x_1,...,x_n$
and by $B(P,Q)$ the Bezout matrix (Bezoutiant) of $P$ and $Q$. A relationship
between the corresponding principal minors, counted from the right-hand lower
corner, of the matrices $B(P,Q)$ and $\Delta(Q)$ is established. It implies
that if the principal minors of the matrix of divided differences of a function
$g(x)$ are positive or have alternating signs then the roots of the Newton's
interpolation polynomial of $g$ are real and separated by the nodes of
interpolation.
