Page 3: Special Cases and Solution Methods

This page covers special cases in quadratic inequalities and provides a systematic approach to solving them.

It explains how to handle cases where the discriminant (Δ = b² - 4ac) is zero, positive, or negative, affecting the nature of the roots.

Definition: The discriminant (Δ) determines the nature of the roots:

• Δ > 0: Two distinct real roots
• Δ = 0: One repeated real root
• Δ < 0: No real roots

The page provides a comprehensive schema disequazioni di secondo grado (scheme for quadratic inequalities), showing how to approach different cases based on the inequality sign and the parabola's orientation.

Example: For x² - 2x + 1 ≤ 0, we find that Δ = 0, leading to one repeated root at x = 1.

The page also includes a table summarizing the solutions for various scenarios, making it easier for students to understand and apply the concepts.

Highlight: The formula disequazioni secondo grado (formula for quadratic inequalities) depends on the sign of the leading coefficient and the nature of the roots.

This comprehensive guide provides students with the tools to solve various types of disequazioni di secondo grado esercizi (quadratic inequality exercises), including those involving disequazioni di secondo grado fratte (fractional quadratic inequalities).