The b2 − 4ac part of the formula is called the discriminant. What happens if the discriminant is

greater than 0?
equal to 0?
less than 0?

since the roots involve -b±√(b^2-4ac)

if the discriminant is negative, there are no real roots.
see what you can make of the other cases
Or, heck -- read your text or use google

In the quadratic formula, the discriminant is the part of the formula given by b^2 - 4ac. It plays an important role in determining the nature of the solutions to a quadratic equation. Let's consider the different cases based on the value of the discriminant:

1. If the discriminant is greater than 0, it means that the expression b^2 - 4ac is positive. This case occurs when the quadratic equation has two distinct real solutions. Mathematically, it means that there are two different values of x that satisfy the quadratic equation. Geometrically, when graphed, the quadratic equation will intersect the x-axis at two distinct points.

2. If the discriminant is equal to 0, it means that the expression b^2 - 4ac equals zero. In this case, the quadratic equation has exactly one real solution. Mathematically, it means that there is a single value of x that satisfies the equation. Geometrically, when graphed, the quadratic equation will touch the x-axis at a single point, which is called a "double root."

3. If the discriminant is less than 0, it means that the expression b^2 - 4ac is negative. In this case, the quadratic equation has no real solutions. Mathematically, it means that there are no real values of x that satisfy the equation. Geometrically, when graphed, the quadratic equation will not intersect the x-axis, indicating that there are no real solutions.

To summarize:
- If the discriminant is greater than 0, the quadratic equation has two distinct real solutions.
- If the discriminant is equal to 0, the quadratic equation has one real solution (a "double root").
- If the discriminant is less than 0, the quadratic equation has no real solutions.