  In 2003, Alfred Menezes, Edlyn Teske and Annegret Weng presented a conjecture
on properties of the solutions of a type of quadratic equation over the binary
extension fields, which had been convinced by extensive experiments but the
proof was unknown until now. We prove that this conjecture is correct.
Furthermore, using this proved conjecture, we have completely determined the
null space of a class of linear polynomials.
