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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