Key Idea: Two Solutions (Quadratic System)

A quadratic system or equation has two real solutions when the discriminant is positive.

General Rule:

• Discriminant formula:

  D=b^2−4ac

• If D>0, there are two distinct real solutions.

• On a graph, this means the parabola intersects the line (or x-axis) at two points.

Why this matters for the SAT:

Understanding the discriminant helps you predict the number of solutions without solving completely.
It’s a fast way to analyze quadratic equations and systems efficiently.