Existence of pair of primitive elements over finite fields of characteristic 2

In this article, we give a sufficient condition for the existence of a primitive element α in F2k such that f(α) is also primitive in F2k, where f(x)=ax2+bx+cdx2+ex+f∈F2k(x) with a,d≠0. Subsequently, using this condition we derive the values of k for which F2k contains primitive pairs of the form (α,f(α)) for f(x)=ax2+bx+cdx2+ex+f and a,d≠0.