  We study a single field inflationary model modified by a non-minimal coupling
term between the Ricci scalar $R$ and the scalar field $\varphi$ in the context
of constant-roll inflation. The first-order formalism is used to analyse the
constant-roll inflation instead of the standard methods used in the literature.
In principle, the formalism considers two functions of the scalar field,
$W=W(\varphi)$ and $Z=Z(\varphi)$, which lead to the reduction of the equations
of motion to first-order differential equations. The approach can be applied to
a wide range of cosmological situations since it directly relates the function
$W$ with Hubble parameter $H$. We perform the inflationary analysis for
power-law and exponential couplings, separately. Then, we investigate the
features of constant-roll potentials as inflationary potentials. Finally, we
compare the inflationary parameters of the models with the observations of CMB
anisotropies in view of realize a physically motivated model.

General Relativity and Quantum Cosmology;High Energy Physics - Theory