  Inspired by the newly observed $X_{0}(2900)$ and $X_1(2900)$ at LHCb, the
$K^*\bar{D}^*$ and $K\bar{D}_1$ interactions are studied in the quasipotential
Bethe-Salpeter equation approach combined with the one-boson-exchange model.
The bound and virtual states from the interactions are searched for as the
poles in the complex energy plane of scattering amplitude. A bound state with
$I(J^P)=0(0^+)$ and a virtual state with $0(1^-)$ are produced from the
$K^*\bar{D}^*$ interaction and $K\bar{D}_1$ interaction, and can be related to
the $X_{0}(2900)$ and $X_1(2900)$ observed at LHCb, respectively. A bound state
with $I(J^P)=0(1^+)$ and a virtual state with $I(J^P)=0(2^+)$ are also
predicted from the $K^*\bar{D}^*$ interaction with a small $\alpha$ value,
which can be searched in future experiments.
