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Math Help - Simplification of root finding problem

  1. #1
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    Simplification of root finding problem

    Hi,
    I was wondering whether there is any simplification available to find roots for something like
    <br />
\sum_{j=0}^n A_j(t) = 0.<br />

    where,
    <br />
A_n(t) = \frac{p_{n2} t^2 + p_{n1} t + p_{n0}}{q_{n2} t^2 + q_{n1} t + q_{n0}}<br />


    Thanks
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  2. #2
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    Opalg's Avatar
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    Quote Originally Posted by krindik View Post
    Hi,
    I was wondering whether there is any simplification available to find roots for something like
    <br />
\sum_{j=0}^n A_j(t) = 0.<br />

    where,
    <br />
A_n(t) = \frac{p_{n2} t^2 + p_{n1} t + p_{n0}}{q_{n2} t^2 + q_{n1} t + q_{n0}}<br />
    Almost certainly not. Equations of the form \sum_{j=0}^n A_j(t) = 0 would include (as a very special case) anything of the form at^2 + bt + c + \frac dt + \frac e{t^2} = 0. So any general method for solving such equations would include a method for solving the general quartic equation. To say the least, that would make it quite an elaborate procedure.
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  3. #3
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    Thanks a lot.
    Infact A_n(t) have the exact same form below.

    <br />
A_n(t) = \frac{(x-a_n) t^2 + (y-b_n) t + b_n^2}{ (y-a_n)^2 t^2 + 2(x-a_n) t + 2b_n}<br />

    The parameters p, q consists of only x, y and a_n, b_n differ for each A_n.
    So isnt there any simplification i can do so that roots in terms of x and y can be found?
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