The Judgement of Roots of Quadratic Equations over a Field with p~k Elements
Sun Zong-ming · Journal of Taishan University · 2010
In this paper,let F be a field with pk elements,0 be the zero element of F and e be the unit element of F.Let ax2+bx+c=0(a≠0) be an equation over F.Using theory of extension field,the author discusses this equation,completely gives its roots,that is,it has two distinct roots or two same roots,and it has no roots.The author sets necessary and sufficient conditions that the equation has roots,and defines judgement expression of roots.At the same time,the author studies other two classes of equations,too.