Calculating the first m + 1 partial quotients of the unique positive root of a trinomial axn + bx + c
We are dealing with polyomial f(x) = axn + bx + c with integer coefficients, a > 0, c < 0. This will have a unique positive root α which we will assume is greater than 1.
The method of Lagrange (1797) is used to find the the first m + 1 partial quotients of α.
We remark that Disc(f(x)) is given by
Disc(f(x)) = an-2(γnncn-1a + β(n-1)n-1bn),
where γ = (-1)n(n-1)/2 and β = (-1)(n-1)(n-2)/2.
For a program that develops the continued fraction of all real roots of a suitably general polynomial, see CALC.
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Last modified 21st July 2006
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