Re: x²+4x+5=0

Op 22/01/2025 om 14:48 schreef Richard Hachel:

x²+4x+5=0
 This equation has no root, and it never will.
 We can then find two roots of its mirror curve.
 Let x'=-3 and x"=-1
 These are not roots of this curve, but the roots of the imaginary mirror curve.
 What is this imaginary mirror curve?
 It is the curve with equation y=-x²-4x-3
 Let's look for its roots, and we find x'=-3 and x'=-1
 These are the imaginary roots of x²-4x+5.
 Or x'=-3(i) and x'=-1(i)
 R.H.

Wolfram Alpha tells us there are two roots:
https://www.wolframalpha.com/input?i=solve+x%5E2%2B4x%2B5%3D0
Here you can see the roots:
https://www.desmos.com/3d/mpwj5h2ab8