Chapter 3 - Section 3.4 - Real Zeros of Polynomials - 3.4 Exercises - Page 283: 4

False.

False. When $a$ is an upper bound but negative, $-a$ will be positive and can not be a lower bound because the lower bound need to be below the upper bound. Even if $a$ is positive, it is not necessarily that $-a$ be a lower bound because the lower bound can be further below $-a$