If I told you a certain polynomial P(x) had a double root (only one!), how could you go about finding it, WITHOUT trying to find every root? Also, the EXACT value of the root is sought; not an approximation.

NB. Roots may be any kind --real or complex-- but they are all different, with multiplicity "1", except for one that has multiplicity "2".

If P(x) has root a1 with multiplicity m1>1, root a2 with multiplicity m2>1, ... ak with multiplicity mk>1, then Pī(x) will have root a1 with multiplicity m1-1, a2 with m2-1, ... ak with mk-1, so if we find the GCM of P(x) and Pī(x), it will have all the repeated roots with multiplicity 1 less than in P(x).

Posted by e.g. on 2006-05-08 15:39:57