Quadratic Extensions

Summary In this article we further develop field theory [6], [7], [12] in Mizar [1], [2], [3]: deal with quadratic polynomials and extensions [5], [4]. First introduce polynomials, their discriminants prove the midnight formula. Then show that - case discriminant of p being non square adjoining a root ’s results splitting . Finally these are only degree 2, e.g. an extension E F is if there Element ∈ such ( F a F\sqrt ) isomorphic over