The Discriminant
What Does the Discriminant Mean?
The sign of the discriminant tells you how many real roots a quadratic equation has before you solve it.
Three possible discriminant results
If Δ > 0, there are two distinct real roots. If Δ = 0, there is one repeated real root. If Δ < 0, there are no real roots.
Interpret the discriminant
- Calculate Δ = b² − 4ac.
- Compare the result with zero.
- State the number and type of real roots.
- Remember that this predicts roots; it does not give their values.
Worked example
Interpret Δ = −8
- −8 is less than zero.
- A negative discriminant makes the square root term non-real.
The quadratic has no real roots.
Common mistakes
- Saying Δ = 0 means zero roots.
- Confusing the discriminant value with a root.
- Claiming two roots without checking whether they are distinct.
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