The dielectric properties and various pattern-forming states of dual-frequency material in a nematic phase, as well as its mixture containing low concentrations of reactive monomers, are reported. The dielectric relaxation behaviors of nematic MLC 2048 are presented and compared to its mixture containing both mesogenic and nonmesogenic reactive monomers. The sign-inversion frequency of the dielectric anisotropy was significantly shifted on the addition of small amounts of the reactive monomers. However, all three mixtures used in this study essentially exhibited the same field-induced instabilities at different frequencies and voltage domains of the applied electric field. A broad band of modulated states were found to exist above a critical voltage and within a voltage dependent frequency band in the vicinity of the sign-inversion frequency, $f_I$, of the dielectric anisotropy. As the $f_I$ of the mixtures shifted, so did the bands of the modulated state of the different mixtures and the temperatures, which were well matched with the measured $f_I$ value.