How to find the roots of a sum of divisions of polynomials

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How can I find those x values in which this function becomes f(x)=0?
I have 4 vectors of length N: A, B, C, D, and
f(x) = sum( ( x*A_i - B_i ) / ((x*C_i - D_i)^3) )

Accepted Answer

Torsten
Torsten on 1 Aug 2019
Edited: Torsten on 1 Aug 2019
Multiply by
prod (x*C_i - D_i)^3
and determine the roots of the resulting polynomial of degree 3*(N-1)+1 using the "roots" command.
You might want to use symbolic computations in advance using expand, collect, and subst to get the numerical coefficients of this polynomial.

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