Thread: Descartes' Rule of Signs Help

I need help figuring out this problem:

Use Descartes' Rule of Signs to analyze the number of positive and negative real roots and the number of non-real roots of the function:

There are at least __ and at most ___ positive real roots.
There are at least___ and at most___ negative real roots.
There are at least ___and at most ____ non-real roots.

Originally Posted by badandy328

I need help figuring out this problem:

Use Descartes' Rule of Signs to analyze the number of positive and negative real roots and the number of non-real roots of the function:

There are at least __ and at most ___ positive real roots.
There are at least___ and at most___ negative real roots.
There are at least ___and at most ____ non-real roots.

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