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(z1,0,z3,0,z)=0 implies for s st s=-(z3/z1) holds z=0
or z=sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2))/2)+ (sqrt ((-Re s+sqrt ((Re s)^2+(
Im s)^2))/2))*<i> or z=-sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2))/2)+ (-sqrt ((-Re
s+sqrt ((Re s)^2+(Im s)^2))/2))*<i> or z= sqrt (( Re s+sqrt ((Re s)^2+(Im s)^2)
)/2)+ (-sqrt ((-Re s+sqrt ((Re s)^2+(Im s)^2))/2))*<i> or z=-sqrt (( Re s+sqrt
  ((Re s)^2+(Im s)^2))/2)+ (sqrt ((-Re s+sqrt ((Re s)^2+(Im s)^2))/2))*<i>
proof
  assume that
A1: z1<>0 and
A2: Polynom(z1,0,z3,0,z)=0;
  let s;
  0 =(z1*z^2+z3)*z by A2;
  then
A3: Polynom(z1,0,z3,z)=0 or z=0;
  assume s=-(z3/z1);
  hence thesis by A1,A3,Th25;
end;
