How to solve a cubic with 2 square terms multiplie by each other?

I am trying to solve G^3 -G^2F^2 +1 =0,

I have F values varying between 1.5 and 4. Normally I would do s=(1 -1 0 1) and then roots of s but i do not know how to display the term shown where the question marks are inserted.(s=(1 -1*(??) 0 1)

Any help is much appreciated.