Δ > 0
- Input
- a=1, b=5, c=4
- Expected output
- Δ = 9
Two real roots: −1 and −4.
calculate discriminant quadratic equation
Calculate Discriminant (Δ) of Quadratic Equation
The discriminant Δ = b²−4ac determines the nature of roots without computing the square root. It is the first step of the quadratic formula.
How to interpret the discriminant
- Δ > 0: two distinct real roots. Δ = 0: one double real root (the parabola touches the x-axis at exactly one point). Δ < 0: no real roots (the parabola does not cross the x-axis).
Examples
Safe use
- Input
- context + tool result
- Expected output
- interpreted with limits and next steps
Use the result as technical or educational support, keeping the tool limits explicit in the workflow.
Full tool FAQ
The discriminant Δ = b²−4ac determines the nature of roots: Δ>0 → two distinct real roots; Δ=0 → double root; Δ<0 → no real roots.
Frequently asked questions
Can Δ be fractional?
Yes. Δ can be any real number. The interpretation (positive/zero/negative) still applies.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.