You are given a polynomial of degree two in , . A convenient way of writing it is in the form where and are its roots, this is, the numbers such that the polynomial is zero.
Now the reasoning: Because the polynomial is a continuous function, these two numbers set a change of sign in the expression . So you should check whether is positive or negative if is greater or smaller than and .
Also for the absolute value condiction this means
Essentially, you are asked to solve an inequality: . And the simplest way to do that is to solve the associated equation. As Ruun suggests, we can factor . So where is that equal to 0? Those points separate "> 0" from "< 0". Just pick one value in each interval to see whether it is "> 0" or "< 0".