Re: y=f(x)=(x²)²+2x²+3

Le 06/02/2025 à 20:15, sobriquet a écrit :

Op 06/02/2025 om 16:42 schreef Richard Hachel:

Bonjour les amis !
 I asked for the roots of the following equation on the French forums, I only got one answer that didn't satisfy me, and the rest is just contempt and insults.
So I'm trying my luck here.
 y=f(x)=(x²)²+2x²+3
 Il y a pour moi, deux racines très simples pour cette équation, dont aucun n'est réelle.
 Can the Anglo-Saxons find these two roots?
 R.H.
 

 Actually there are four complex roots.
 https://www.wolframalpha.com/input?i=x%5E4%2B2x%5E2%2B3

 Yes, these are indeed the roots found in traditional development.
Mathematicians find four complex roots.
Personally, in this specific case, I only find two, because I think there are only two.
But I use different concepts, and a different method.
For me, the roots are x'=-i and x"=i in this particular case, and I place them on the y=0 axis, obviously, and on a simple Cartesian coordinate system.
DON'T SHOUT!
I remind you that I use a different approach that I think is more correct and in line with the very nature of i, and its precise definition, which is not only i²=-1.
R.H.