The discriminant Δ in the quadratic equation is given by:
- Δ = b2 − 4ac
The discriminant can be used to provide information about the number of solutions to a quadratic equation:
- if Δ > 0, there are two unique real solutions
- if Δ = 0, there is one unique real solution
- if Δ < 0, there are no unique real solutions.
Suppose one needed to find solutions for the equation x2 − 6 = x.
First we rearrange the equation to make it equal zero:
- x2 − 6 = x
Now, using the quadratic formula:
- or .