Hello,
Is there any way to solve polynomial equations of the form:
?
I really hope so.
PS- it probably doesn't matter, but for the particular problem I have in mind, , where "i" is the imaginary unit.
Well that's not a polynomial then, since it has non-integer exponents. I guess it could *perhaps* be boiled down to a cubic, but I'm not sure if that is still valid if we have a complex number as an exponent.
Anyway, if you can't solve it, it should remain continuous and derivable regardless of what "u" is, so if you can't find an algebraïc way do to it, you can just use a Newton approximation and solve for x
Newton approximation eh? I'll have to look that up.
In the meantime, what about this idea...
Say d is actually d(x), that is to say, d is a function of x...
(we know that d(1) is defined)
Now say I divide the argument of d(x) by x. Since I have to do this to all x's, wouldn't this then yield...
Then multiplying through by ...
Would that work?