Re: x²+4x+5=0

On 1/22/2025 3:58 PM, sobriquet wrote:

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

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

The roots are fun to work with in a Julia fractal. They can plot many things. An example, my multi julia:
https://paulbourke.org/fractals/multijulia