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Repeated Root Research (Posted on 2006-05-08) Difficulty: 3 of 5
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".

See The Solution Submitted by Old Original Oskar!    
Rating: 3.6667 (3 votes)

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Solution A most general solution | Comment 2 of 7 |
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
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