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We study a mixture of a dipolar condensate and a degenerate Fermi gas in aquasi-one-dimensional geometry. We demonstrate that the presence of fermionsmay drastically change the behavior of a dipolar condensate. For strong enoughboson-fermion attraction a dipolar Bose-Fermi droplet appears in the mixtureand a roton excitation develops in the Bogoliubov excitations spectrum. Asshown analytically and by solving numerically the coupled set of extendedGross-Pitaevski and Hartree-Fock equations for bosonic and fermioniccomponents, respectively, roton instability mechanism leads to the formation ofsupersolid phase in a Bose-Einstein condensate. Scaling arguments show thatalthough the dysprosium atoms are considered to demonstrate the appearance ofthe supersolid phase, such a phase can be observed with less magnetic atomslike chromium and even rubidium.

Supersolidity of dipolar Bose-Einstein condensates induced by coupling to fermions