Could anyone help me with the following problem:

Write a VBA function that computes one real-valued root of the polynomial defined by

P(x) = (summation mark goes from i = 1 to n) coeffs.cells(i,1) x^(powers.cells(i,1))

where n=coeffs.Rows.Count using Newton's Solver. For the input, coeffs is a Range with n rows (and 1

column) of real-valued coefficientcients, and powers is a Range with n rows (and 1 column) of non-negative,

integer powers.

I guess ''Newton's Solver'' is actually the Newton-Raphson algorithmn.

My solution so far is:

Function polySolver(coeffs As Range, powers As Range) As Double

Dim rowCount As Integer

Dim i As Integer

Dim xn As Double

Dim xnm1 As Double

Dim fx As Double

fx = 0

Dim fxprime As Double

fxprime = 0

xnm1 = 0.1

rowCount = coeffs.Rows.count

Do

For i = 1 To rowCount

fx = fx + coeffs.Cells(i, 1) * xnm1 ^ powers.Cells(i, 1)

fxprime = fxprime + (powers.Cells(i, 1) * coeffs.Cells(i, 1)) * xnm1 ^ _

(powers.Cells(i, 1) - 1)

Next i

xn = xnm1 - fx / fxprime

xnm1 = xn

Loop Until (Abs(fx) < 0.00001)

polySolver = xn

End Function

When I choose different initial values of x0 (in the code denoted with xnm1), I get different solutions. This function probably shouldn't even contain the initial x0 (I suppose that the should't have an assigned value for xnm1). The algorithmn should be valid for any polynomial and the outcome should be one real-valued root of this polynomial.