Polynomial inverion based polynom a b c d

[xeroc]

Hello,

I am new in this forum and i am french.
I search inverse a polynomial beginning from an exist a polynomial.
I have a polynomial :
A = 1
B = -2
C = 5
D= 50
Y=Ax^3+Bx^2+Cx+D
I want :
P ?
Q ?
R ?
S ?
X=Px^3+Qx^2+Rx+S

I want used formula Excel.

Help me please.

Thank you in advance for your support.

PS : My english is not good, sorry

[Andy Pope]

For information see
http://tushar-mehta.com/publish_trai...nalysis/16.htm

[MrShorty]

This question makes me think this is part of a school assignment. If this is true, and you explain where you are at in your math studies, we might be able to give an answer that will fit into the course material in way that will help you understand what you are being taught.

A regression approach as suggested might be the easiest in Excel - it is an approach that I have used many times. However, if this is schoolwork, it might not help you learn what you are supposed to be learning with this exercise.

One thing to be aware of - Not every cubic polynomial will have an inverse. Here's a good discussion http://www.wmueller.com/precalculus/...c/invpoly.html

In this link, he suggests that the general method for finding the inverse is to find the roots of the function g(x)=f(x)-y. When I was in school, it was generally felt that numerical methods (like the Newton-Raphson method) were necessary for finding the roots of generic cubic equations. Wikipedia shows some expressions for the roots of cubic equations which are quite complex. Perhaps, after determining that an inverse function exists, these expressions may lead you to your inverse function.