Recently, the τ→Kπντ decay spectrum has been measured by the Belle and BaBar collaborations. In this work, we present an analysis of such decays introducing a dispersive parametrization for the vector and scalar Kπ form factors. This allows for precise tests of the Standard Model. For instance, the determination of f+(0)|Vus| from these decays is discussed. A comparison and a combination of these results with the analyses of the Kℓ3 decays is also considered.