reserve
F for non 2-characteristic non quadratic_complete polynomial_disjoint Field;
reserve
p for non DC-square quadratic Element of the carrier of Polynom-Ring F;

theorem Z2:
for a being non zero Element of FAdj(F,{sqrt(DC p)}),
    b,c being Element of FAdj(F,{sqrt(DC p)})
st p = <%c,b,a%>
holds Root1 p = (-b + (RootDC p)) * (2 '*' a)" &
      Root2 p = (-b - (RootDC p)) * (2 '*' a)"
proof
let a be non zero Element of FAdj(F,{sqrt(DC p)}),
    b,c be Element of FAdj(F,{sqrt(DC p)});
reconsider E = FAdj(F,{sqrt(DC p)}) as
       F-extending FieldExtension of FAdj(F,{sqrt(DC p)}) by FIELD_4:6;
assume  p = <%c,b,a%>; then
H: p.1 = b & p.2 = a by qua1;
A: @(b,E) = b & @(a,E) = a by FIELD_7:def 4; then
   @(b,E) = @(p.1,E) by H,FIELD_7:def 4;
hence thesis by A,H,FIELD_7:def 4;
end;
