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"No Solution (Quadratic System)" Explained

Discriminant (b^2-4ac) is less than zero (a negative number).

Key Idea: No Solution (Quadratic System)

A quadratic system has no real solution when the equation has no points of intersection.

General Rule:

  • Use the discriminant:

Δ=b^2−4ac

  • If Δ<0 (negative), the quadratic has no real solutions.

Why this matters for the SAT:

Discriminants help quickly determine the number of solutions without solving the equation fully. This is essential for analyzing quadratic graphs and systems efficiently.