  Unitarity of scale-invariant coupled theory of higher-derivative gravity and
matter is investigated. A scalar field coupled with dirac fermion is taken as
matter sector.Following the idea of induced gravity Einstein-Hilbert term is
generated via dynamical symmetry breaking of scale-invariance. The
renormalisation group flows are computed and one-loop RG improved effective
potential of scalar is calculated. Scalar field develops a new minimum via
Coleman-Weinberg procedure inducing Newton's constant and masses in the matter
sector. The spin-2 problematic ghost and the spin-0 mode of the metric
fluctuation gets a mass in the broken phase of theory. The energy-dependence of
VeV in the RG improved scenario implies a running for the induced parameters.
This sets up platform to ask whether it is possible to evade the spin-2 ghost
by keeping its mass always above the running energy scale? In broken phase this
question is satisfactorily answered for a large domain of coupling parameter
space where the ghost is evaded. The spin-0 mode can be made physically
realisable or not depending upon the choice of initial parameters. Induced
Newton's constant is seen to vanishes in ultraviolet. By properly choosing
parameters it is possible to make the matter fields physically unrealisable.
