Re: Roots of a second degree equation.

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Sujet : Re: Roots of a second degree equation.
De : acm (at) *nospam* muc.de (Alan Mackenzie)
Groupes : sci.math
Date : 22. Jan 2025, 11:28:11
Autres entêtes
Organisation : muc.de e.V.
Message-ID : <vmqh7r$874$1@news.muc.de>
References : 1
User-Agent : tin/2.6.3-20231224 ("Banff") (FreeBSD/14.1-RELEASE-p5 (amd64))
Richard Hachel <r.hachel@liscati.fr.invalid> wrote:
Roots of a quadratic equation.

y=ax²+bx+c

If b² >4ac then there are two roots.

If b=4ac then there is a single root.

If b²<4ac there are no roots.

We can then draw as many curves as we want, as long as we want, nothing
will change, there are no roots.

At least in the real world.

Let us set y=x²+1 or y=x²+4x+5; there are no roots.

This does not exist, looking for roots in nothingness, or rabbit horns
will not change anything. We will not find any.

Some mathematicians will then try to find some anyway, but beyond reality,
where Doctor Hachel takes possession of your computer screen and will give
it back to you only if he wants to (I put a virus in the equation
mentioned above).

They call these imaginary roots, because, since they do not exist, we must
imagine them. But what do they correspond to?

What exactly do you mean by saying that the imaginary roots (usually
called complex roots by mathematicians) do not exist?  What attribute
does -2 + i possess, or lack, that entitles you to attribute to it the
property of non-existence?  How does -2 + i differ in that respect from
other numbers such as -1 or 42?

The fact is, there is a vast theory of complex analysis which is
coherent and fascinating.  It is also useful in science and engineering.

[ .... ]

R.H.

--
Alan Mackenzie (Nuremberg, Germany).


Date Sujet#  Auteur
22 Jan 25 * Roots of a second degree equation.3Richard Hachel
22 Jan 25 `* Re: Roots of a second degree equation.2Alan Mackenzie
22 Jan 25  `- Re: Roots of a second degree equation.1Moebius

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