  Let X be a projective hypersurface in P_k^n of degree d <= n. In this paper
we study the relation between the class [X] in K_0(Var_k) and the existence of
k-rational points. Using elementary geometric methods we show, for some
particular X, that X(k) is nonempty if and only if [X] is equivalent to 1
modulo the class of the affine line in K_0(Var_k). More precisely we consider
the following cases: a union of hyperplanes, a quadric, a cubic hypersurface
with a singular k-rational point, and a quartic which is a union of two
quadrics one of which being smooth.
