  For any natural $d \ge k \ge 2$ we calculate the cohomology groups of the
space of homogeneous polynomials $R^2 \to R$ of degree $d$, which do not vanish
with multiplicity $\ge k$ on real lines. For $k=2$ this problem provides the
simplest example of the situation, when the "finite degree" invariants of
nonsingular objects are not a complete system of invariants.
