  We calculate the excitation spectrum of a one-dimensional self-bound quantum
droplet in a two-component bosonic mixture described by the Gross-Pitaevskii
equation (GPE) with cubic and quadratic nonlinearities. The cubic term
originates from the mean-field energy of the mixture proportional to the
effective coupling constant $\delta g$, whereas the quadratic nonlinearity
corresponds to the attractive beyond-mean-field contribution. The droplet
properties are governed by a control parameter $\gamma\propto \delta g
N^{2/3}$, where $N$ is the particle number. For large $\gamma>0$ the droplet
features the flat-top shape with the discrete part of its spectrum consisting
of plane-wave Bogoliubov phonons propagating through the flat-density bulk and
reflected by edges of the droplet. With decreasing $\gamma$ these modes cross
into the continuum, sequentially crossing the particle-emission threshold at
specific critical values. A notable exception is the breathing mode which we
find to be always bound. The balance point $\gamma = 0$ provides implementation
of a system governed by the GPE with an unusual quadratic nonlinearity. This
case is characterized by the ratio of the breathing-mode frequency to the
particle-emission threshold equal to 0.8904. As $\gamma$ tends to $-\infty$
this ratio tends to 1 and the droplet transforms into the soliton solution of
the integrable cubic GPE.
