The coeficients of change sign times, hence there are at most

positive roots of . As the number of positive roots can only change by

multiples of the minimum number of real roots is .

The coefficients of change sign times, thus there are at most

negative roots of , and the minimum number is .

As and there are a total of real or non-real roots there may be as

few as non-real roots. The maximum number is (when there is one real

root).

RonL