I am new to this forum and Mathematica and could really use your help [and patience].
My ultimate goal is to get a simple 4th degree polynomial equation that I can code into a program. Here is the method I'm using to acheive this goal:
I have an equation
y = x + x^2 + x^3 + x^4
that I need to solve for multiple positive values of y. For example, I used
Solve[x + x^2 + x^3 + x^4 == .55]
which gives me x=0.358668 [I'm only interested in the positive value of x]. For my analysis, y can range between 0 and 100. I started to manually change it's value .05 at a time, plugging it into Solve and writing down each of the calculated values. This is obviously very manually intensive.
Once I got enough values to see if it would work [48 in this case], I used regression analysis in Excel to create an equation
k = -0.0075j^4 + 0.0706j^3 - 0.2737j^2 + 0.6621^j + 0.0672
that I can code in my program. I need a more efficient way to do this and thought that I could do it all in Mathematica...
- for y=0 to 100, step .05, solve for x where y = x + x^2 + x^3 + x^4 [this would produce a dataset of y and x values where the y values go from 0, 0.05, 0.10, 0.15, ... 99.95, 100.0 and a corresponding x value is generated from solving the equation]
- using the output dataset from above and regression analysis, create a 4th degree polynomial equation like k above.
- is this doable in Mathematica?
Any help/suggestions would be greatly appreciated.