For the first, you have this. For the second, you have this. For the third, in general, the quintic polynomial is not solvable (that's been proved, actually). Certain special cases can be solved, but not the general quintic.
Hello there!
In my work, I will have to convert functions. My English is crap, so I will just show you what I mean.
If I have a function:
y = x + 1 i can convert it to look like this: x = y - 1. I would like to do the same for:
y = x^3 + x^2 + x + 1
or this:
y = x^4 + x^3 + x^2 + x + 1
or this:
y = x^5 + x^4 + x^3 + x^2 + x + 1
How is that done?
Thank you.
Kind regards,
Marius
For the first, you have this. For the second, you have this. For the third, in general, the quintic polynomial is not solvable (that's been proved, actually). Certain special cases can be solved, but not the general quintic.
This is a cubic.
This is a quartic.or this:
y = x^4 + x^3 + x^2 + x + 1
This is a quintic.or this:
y = x^5 + x^4 + x^3 + x^2 + x + 1
I don't know where you found your "cubic" formula, but it's not nearly complicated enough for a cubic. It looks like an incorrect quadratic. Here's the solution for your cubic. Here's the solution for your quartic.How is that done?
Thank you.
Kind regards,
Marius
Really? I didn't know that! Just doing a simple google search brought up the Jacobi theta function method, as well as hypergeometric functions (hypergeometric functions do seem to show up lots of different places, don't they? Maybe that's why the Russians do everything in terms of them.), as possibilities for solving the general quintic.