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