A polynomial
 <i>f</i>(<i>x</i>)
over a field <I>F</I>
 has a multiple zero in some extension field <I>E</I> if
and only if  <i>f</i>(<i>x</i>)
  and its derivative  have a common factor of positive degree in
 <I>F</I>[<I>x</I>].