Question

Locating Zeros of Polynomial Function:

Answer 1

The value p is an upper bound on the real roots of the polynomial if division of the polynomial by (x-p) results in quotient terms that all have positive coefficients.

The value q is a lower bound on the real roots of the polynomial if division of the polynomial by (x-q) results in quotient terms that alternate signs.

_____

The division can be either synthetic division or long division.

_____ ______

An upper bound on the magnitude of the roots can be found this way:

• Divide all coefficients by that of the highest-degree term
• Find the absolute value of the result
• Choose the maximum of those results and increase it by 1

There are various refinements, including finding the sum of the ratios of successive coefficients, or taking increasing roots of the ratios found above, then doubling the maximum of those.

Answer 2

Use synthetic division to find the values of the polynomial function for consecutive integers. An integer that produces no sign change in the quotient and the remainder is an upper bound. To find a lower bound of a function, find an upper bound for the function of -x. The lower bound is the negative of the upper bound for the function of -x.

That is the right answer as I just finished the 10 practice problems on E2020