Re: Reference for a cubic with a double root?

From: R3769 (r3769_at_aol.com)
Date: 08/11/04 

Date: 11 Aug 2004 17:48:31 GMT

>[I see that this is done in (my Aristotle University professor) Konstantinos
>Lakkis's "Algebra" (1976), but that book is written in Greek, and I need a
>reference in English; C. C. MacDuffee's "Theory of Equations" (1954) comes
>close to what I need in Theorem 50* (p. 91), except that he assumes a = 1
>(a very minor offense which I would still prefer to avoid if possible).]
>
>*With D = (b^2)(c^2) - 4(c^3) - 4(b^3)d - 27(d^2) + 18bcd, the cubic
>x^3 + bx^2 + cx + d has a double (real) root in case D = 0, three distinct
>real roots in case D > 0, and precisely one real root in case D < 0 : there
>is a reason that D is called "discriminant", in case you forgot :-)
>

Perhaps what you need can be found in L. E. Dickson's "New First Course in the
Theory of Equations" (1939) Th 3, Ch V, pg 47.

Rich

> baloglouAToswego.edu
>
>One possible reason for the creature's sudden fit of fury may have been an
>unconfirmed report that it was "kicked by somebody in business class" on
>its way through the cabin [http://news.bbc.co.uk/2/hi/europe/3551672.stm]
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