Quadratic Discriminant
Calculator
Results
- Discriminant (Δ)
- 1
- Number of real roots
- 2
- First root
- 3
- Second root
- 2
- Vertex x
- 2.5
Results
| Discriminant (Δ) | 1 |
| Number of real roots | 2 |
| First root | 3 |
| Second root | 2 |
| Vertex x | 2.5 |
formula-map diagram
- Discriminant (Δ)
- 1
- Number of real roots
- 2
- First root
- 3
- Second root
- 2
- Vertex x
- 2.5
Formula map
Formula
Δ = b² − 4 × a × c= 1
Note
Simplified model: these are exact results of the stated idealised formulas, assuming perfect shapes and exact inputs. Real measurements carry error, and the ellipse perimeter is a Ramanujan approximation. Verify independently before relying on these figures.
More in Mathematics
See all →Frequently asked questions
What is the discriminant and what does this calculator need?+
Given a quadratic equation ax² + bx + c = 0, you enter the coefficients a, b, and c. The discriminant is the value Δ = b² - 4ac, which reveals the nature of the equation's roots.
How do I interpret the result?+
If Δ > 0, the equation has two distinct real roots. If Δ = 0, it has exactly one repeated real root. If Δ < 0, it has no real roots — only two complex conjugate roots.
Why is the discriminant useful before actually solving the equation?+
It tells you what kind of answer to expect from the quadratic formula without doing the full calculation — useful for quickly checking whether a real-world problem modeled by the equation even has a real solution.
What if a = 0?+
If a is zero, the equation is no longer quadratic — it becomes linear (bx + c = 0), and the discriminant concept doesn't apply. Most calculators will flag this as invalid input.
How does the discriminant relate to a parabola's graph?+
It tells you how the parabola y = ax²+bx+c relates to the x-axis: two crossings if positive, one tangent touch if zero, and no crossings at all if negative.