The expression $b^2 - 4ac$ is known as the discriminant of a quadratic equation of the form $ax^2 + bx + c = 0$. The value of the discriminant helps determine the nature of the roots of the quadratic equation:

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

Would you like more details or have any questions? Here are some related questions that might interest you:

1. How do you derive the quadratic formula using the discriminant?
2. Can you provide an example of a quadratic equation and calculate its discriminant?
3. What are complex roots and how do they relate to the discriminant?
4. How does the discriminant change the graph of a quadratic function?
5. What is the significance of the discriminant in physics or engineering problems?
6. How can you solve a quadratic equation by completing the square?
7. What happens to the roots of a quadratic equation when the coefficients change?
8. How do you factor a quadratic equation when the discriminant is a perfect square?

Tip: Always check the discriminant first when solving quadratic equations to understand the nature of the roots before proceeding with other methods.