
theorem Th43:
  for L being non degenerated comRing, p being Polynomial of L st
  len p = 1 holds Roots p = {}
proof
  let L be non degenerated comRing, p be Polynomial of L;
  assume len p = 1;
  then
A1: p =<%p.0%> & p.0 <> 0.L by Th16;
  assume Roots p <> {};
  then consider x being object such that
A2: x in Roots p by XBOOLE_0:def 1;
  reconsider x as Element of L by A2;
  x is_a_root_of p by A2,POLYNOM5:def 10;
  then eval(p,x) = 0.L;
  hence contradiction by A1,POLYNOM5:37;
end;
