reserve a,b,c,d,a9,b9,c9,d9,y,x1,u,v for Real,
  s,t,h,z,z1,z2,z3,s1,s2,s3 for Complex;

theorem
  z1<>0 & Polynom(z1,z2,z3,0,z)=0 implies for s,h,t st h=(z2/(2*z1))^2-
z3/z1 & t=z2/(2*z1) holds z=0 or z= sqrt (( Re h+sqrt ((Re h)^2+(Im h)^2))/2)+
(sqrt ((-Re h+sqrt ((Re h)^2+(Im h)^2))/2))*<i>-t or z=-sqrt (( Re h+sqrt ((Re
  h)^2+(Im h)^2))/2)+ (-sqrt ((-Re h+sqrt ((Re h)^2+(Im h)^2))/2))*<i>-t or z=
sqrt (( Re h+sqrt ((Re h)^2+(Im h)^2))/2)+ (-sqrt ((-Re h+sqrt ((Re h)^2+(Im h)
^2))/2))*<i>-t or z=-sqrt (( Re h+sqrt ((Re h)^2+(Im h)^2))/2)+ (sqrt ((-Re h+
  sqrt ((Re h)^2+(Im h)^2))/2))*<i>-t
proof
  assume that
A1: z1<>0 and
A2: Polynom(z1,z2,z3,0,z)=0;
  let s,h,t;
  0 =Polynom(z1,z2,z3,z)*z by A2;
  then
A3: z=0 or Polynom(z1,z2,z3,z)=0;
  assume h=(z2/(2*z1))^2-z3/z1 & t=z2/(2*z1);
  hence thesis by A1,A3,Th26;
end;
