Question

Asked Aug 8, 2019

Step 1

Given information:

The given polynomial function is

Step 2

Given information:

The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is less than it by an even number.

So, the coefficients are 1,-3,-13,15.

There are 2 changes.

This means that there are 2 or 0 positive real roots.

To find the number of negative real roots, substitute x with -x in the given polynomial:

Step 3

The coefficients are -1,-3,13,15.

There is 1 change.

This means that there is 1 negat...

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