Consider the equation .
Let be the number of real roots, be the sum of those roots, and be the product of those roots. What is ?
The set of solutions of the equation is a disjoint union of one or more segments. Find the sum of their lengths.
Lazy Liz doesn't like absolute values notation, and often drops them from her equations. She always writes
How many of the ordered pairs of integers , each of which are between 0 and 10 inclusive, are there, such that
Given that are real numbers that satisfy the system of equations above, what is the sum of all distinct values of ?