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Let
be an univariate polynomial of degree
:
Assume
and let
(
) be the first negative
coefficients of
(if
has no negative coefficients then
there is no positive real root).
The upper bound
of the value of the positive real root is:
where
is the greatest absolute value of the negative coefficients
of
,[3],[13].
If we define:
Then the upper bound of the positive real roots of
is the lower
bound
of the positive real root of
. Consequently if
and
are computed for the polynomial
then
Jean-Pierre Merlet
2012-12-20