Re: New equation

On Mon, 24 Feb 25 21:11:40 +0000, Richard Hachel <r.hachel@tiscali.fr>
wrote:
 

Le 24/02/2025 à 21:23, Barry Schwarz a écrit :

On Mon, 24 Feb 25 18:52:17 +0000, Richard Hachel <r.hachel@tiscali.fr>

>

A quartic always has four roots.

>
Here, I would still put a small caveat.
The fact of saying that an equation of degree n has n roots is perhaps not
entirely correct.
I ask myself the question.
If for example we write f(x)=x^3+3x-4, it is indeed an equation of degree
3.
But how many roots, and what are they?
I asked this question to mathematicians, and to artificial intelligence,
and I was given three roots, but they are incorrect, because those who
answer do not seem to understand the real concept of imaginary numbers.
There is in fact only one root.
A very strange root composed of a real root and a complex root. Both
placed on the same point A(1,0) and A(-i,0).
>
R.H.

 A cubic has three roots.
 The roots of your equation are 1, (-1+i*sqrt(15))/2, and
(-1-i*sqrt(15))/2.
 I have no idea what you mean by a point A(-i,0).