2025-01-1920240129-167X10.1142/S0129167X245001502-s2.0-85186693136https://doi.org/10.1142/S0129167X24500150https://hdl.handle.net/20.500.14288/26594We prove a simple necessary and sufficient condition for a two-bridge knot K(p,q) to be quasipositive, based on the continued fraction expansion of p/q. As an application, coupled with some classification results in contact and symplectic topology, we give a new proof of the fact that smoothly slice two-bridge knots are non-quasipositive. Another proof of this fact using methods within the scope of knot theory is presented in Appendix A, by Stepan Orevkov.MathematicsJournal Article1793-65191178068000001Q351029