  A sequence of $d+1$ signs $+$ and $-$ beginning with a $+$ is called a {\em
sign pattern (SP)}. We say that the real polynomial $P:=x^d+\sum
_{j=0}^{d-1}a_jx^j$, $a_j\neq 0$, defines the SP $\sigma :=(+$,sgn$(a_{d-1})$,
$\ldots$, sgn$(a_0))$. By Descartes' rule of signs, for the quantity $pos$ of
positive (resp. $neg$ of negative) roots of $P$, one has $pos\leq c$ (resp.
$neg\leq p=d-c$), where $c$ and $p$ are the numbers of sign changes and sign
preservations in $\sigma$; the numbers $c-pos$ and $p-neg$ are even. We say
that $P$ realizes the SP $\sigma$ with the pair $(pos, neg)$. For SPs with
$c=2$, we give some sufficient conditions for the (non)realizability of pairs
$(pos, neg)$ of the form $(0,d-2k)$, $k=1$, $\ldots$, $[(d-2)/2]$.
