reserve x,y,a,b,c,p,q for Real;
reserve m,n for Element of NAT;

theorem Th5:
  a <> 0 & Polynom(a,b,0,x) = 0 implies x=0 or x = -(b/a)
proof
  assume that
A1: a<>0 and
A2: Polynom(a,b,0,x) = 0;
  a*x^2+b*x+0=0 by A2,POLYEQ_1:def 2;
  then (a*x+b+0)*x=0;
  then a*x+b+-b=0+-b or x=0 by XCMPLX_1:6;
  then x=(-b)/a or x=0 by A1,XCMPLX_1:89;
  hence thesis by XCMPLX_1:187;
end;
