perplexus.info :: Calculus : Repeated Root Research

Repeated Root Research (Posted on 2006-05-08)

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".

Submitted by Old Original Oskar!

Rating: 3.6667 (3 votes)

Solution: (Hide)

If P(x) has a double root A, then P(x)= (x-A)²Q(x), where Q(A)≠0, and P'(x)= (x-A)[2Q(x)+(x-A)Q'(x)].
If we apply Euclid's algorithm to P(x) and P'(x), their GCD will be (x-A).

Comments: ( You must be logged in to post comments.)

Subject	Author	Date
Puzzle Solution	K Sengupta	2022-12-31 01:49:59
re: Complex not possible	Richard	2006-05-09 14:16:26
Complex not possible	Jer	2006-05-09 13:14:57
re(2): A most general solution	e.g.	2006-05-09 08:18:31
re: A most general solution	Richard	2006-05-08 16:38:38
A most general solution	e.g.	2006-05-08 15:39:57
No Subject	Richard	2006-05-08 13:08:49

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