Let
 <i>f</i>(<i>x</i>)
  be an irreducible polynomial
 <i>f</i>(<i>x</i>) over a field <I>F</I>.   If <I>F</I> has characteristic 0, then
 <i>f</i>(<i>x</i>)
  has no multiple zeros.  If <I>F</I> has characteristic <i>p &#8800 0</i>, then
 <i>f</i>(<i>x</i>)
  has a multiple zero if and only if it is of the form
 <i>f</i>(<i>x</i>)  =  <i>g</i>(<i>x<SUP>p</SUP></i>) for some
 <i>g</i>(<i>x</i>) &#8712 <I>F</I>[<i>x</i>].