The document discusses the discriminant and how it is used to determine the number of solutions to a quadratic equation. It defines the discriminant as b^2 - 4ac and explains that: - If the discriminant is positive, there are 2 solutions - If the discriminant is 0, there is 1 solution - If the discriminant is negative, there are no real solutions. Several examples are provided to demonstrate calculating the discriminant and using it to determine the nature of the roots. The key aspects are to identify the coefficients a, b, and c and then evaluate and compare b^2 - 4ac to determine how many solutions exist.