The quantity $b^2 - 4ac$, found under the radical sign in the quadratic formula, is called the discriminant. The discriminant helps determine the nature of the roots of the quadratic equation $ax^2 + bx + c = 0$.

• If $b^2 - 4ac > 0$, the equation has two distinct real roots.
• If $b^2 - 4ac = 0$, the equation has one real root (a repeated root).
• If $b^2 - 4ac < 0$, the equation has two complex roots.

Would you like more details or have any further questions?

Here are 5 related questions for further exploration:

1. What is the quadratic formula?
2. How do we derive the quadratic formula?
3. Can the discriminant be used to factor a quadratic equation?
4. How does the discriminant affect the graph of a quadratic function?
5. What are complex roots, and how are they represented?

Tip: The discriminant can quickly tell you whether a quadratic equation can be factored using real numbers.