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Discriminant Calculator.

Calculate Δ = b² − 4ac and identify the quadratic root type.

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Result: discriminant: 1.000000 · rootType: two real roots

Result

discriminant: 1.000000 · rootType: two real roots

Use Cases

Check root types before solving

Quickly determine if a quadratic equation has real or complex roots without solving it fully. Useful for homework, exam prep, or verifying solutions.

Example: For x² - 5x + 6 = 0, enter a=1, b=-5, c=6 to see Δ=1, indicating two real roots.

Verify the nature of roots in engineering or physics problems

In applied math, knowing whether a quadratic has real solutions can indicate if a physical scenario is possible. Use the calculator to check conditions before proceeding.

Example: For a projectile motion equation, enter the coefficients to see if the discriminant is positive, ensuring real time solutions.

Frequently Asked Questions

What does the discriminant tell me about a quadratic equation?
The discriminant (Δ) determines the nature of the roots of a quadratic equation ax² + bx + c = 0. If Δ > 0, there are two distinct real roots. If Δ = 0, there is exactly one real root (a repeated root). If Δ < 0, there are two complex (non-real) roots.
How do I use the discriminant calculator?
Enter the coefficients a, b, and c from your quadratic equation in the form ax² + bx + c = 0. The calculator will compute Δ = b² − 4ac and tell you the type of roots based on the value of Δ.
What if the discriminant is zero?
If Δ = 0, the quadratic has exactly one real root (also called a double root). This means the parabola touches the x-axis at a single point.

Tips & Common Mistakes

Tips

  • Ensure the equation is in standard form ax² + bx + c = 0 before entering values. Move all terms to one side if needed.
  • Remember that 'a' cannot be zero; otherwise, the equation is not quadratic.
  • Use the discriminant to quickly check if a quadratic can be factored over real numbers: if Δ is a perfect square, it factors nicely.
  • Double-check the signs of b and c when entering negative coefficients.

Common Mistakes to Avoid

  • Forgetting to include the negative sign when b or c is negative, leading to incorrect Δ.
  • Entering a=0, which makes the equation linear, not quadratic, and the discriminant formula is not applicable.
  • Misinterpreting Δ=0 as 'no roots' instead of 'one real root'.

Last updated: August 13, 2026