Question

Using the discriminant how can you tell how many solutions the quartet has

Answer 1

The discriminant of a quadratic equation in the form of $ax^2 + bx + c = 0$ is given by $b^2 - 4ac$.

If the discriminant is positive, then the equation has two distinct real solutions.
If the discriminant is zero, then the equation has exactly one real solution.
If the discriminant is negative, then the equation has two complex solutions.

Therefore, by evaluating the discriminant of a quadratic equation, you can determine how many solutions it has.