Re: Reference for a cubic with a double root?

From: Acid Pooh (poohonlsd_at_yahoo.com)
Date: 08/10/04 

Date: 9 Aug 2004 23:59:13 -0700

baloglou@panix.com (George Baloglou) wrote in message news:<cf97jv$r4v$1@panix2.panix.com>...
> [reply address is baloglouAToswego.edu]
>
> Following the standard derivation of the formula for the solutions of a
> cubic, it is not hard to see that ax^3 + bx^2 + cx + d = 0 has a double
> root if and only if (2b^3 - 9a*b*c + 27a^2*d)^2 = 4(b^2 - 3a*c)^3. Does
> anyone know of a book where this fact is explicitly mentioned and proven?
>
> Thanks in advance,
>
> baloglouAToswego.edu

I don't have a reference, but it's not too hard to prove (well, a
slightly more difficult problem took me about eight hours, but the
method is relatively quick once you know what it is). Check out:

http://groups.google.com/groups?hl=en&lr=&ie=UTF-8&threadm=d7ba1f79.0404081637.601142b6%40posting.google.com&rnum=1&prev=/groups%3Fq%3D%2522Acid%2BPooh%2522%2Bproblem%2Bdet%26hl%3Den%26lr%3D%26ie%3DUTF-8%26selm%3Dd7ba1f79.0404081637.601142b6%2540posting.google.com%26rnum%3D1

'cid 'ooh