On the multiplicative order of the roots of bXqr+1−aXqr+dX−c

In this paper, we find a lower bound for the order of the group 〈θ+α〉⊂F‾q⁎, where α∈Fq, θ is a generic root of the polynomial FA,r(X)=bXqr+1−aXqr+dX−c∈Fq[X] and ad−bc≠0.