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x²

Quadratische-Gleichungs-Löser

Löst ax²+bx+c=0 mit Diskriminante und Schritten.

x² +
x +
= 0
Equation
x² − 5x + 6 = 0
Discriminant D
1
Root type
Two distinct real roots
Roots
x₁ = 3
x₂ = 2
Steps
  1. Equation: x² − 5x + 6 = 0
  2. Discriminant D = b² − 4ac = (-5)² − 4(1)(6) = 1
  3. D > 0 → two distinct real roots
  4. x = (−b ± √D) / (2a)
  5. x₁ = 3, x₂ = 2

Über Quadratische-Gleichungs-Löser

For ax² + bx + c = 0, the discriminant D = b² − 4ac tells you whether you get two real roots, a repeated root, or a complex conjugate pair. The quadratic formula is easy to mis-sign by hand. Enter a, b, and c to see D, the root type, the roots (complex as a±bi), and short steps. If a = 0 the tool falls back to a linear equation and clearly reports 0 = 0 or no solution. Everything runs in your browser; nothing is sent to toco.tools servers.

So funktioniert's

  1. Enter coefficients a, b, c (or pick a preset)
  2. Read the discriminant and root type
  3. Read the roots and steps (copy if needed)

FAQ

Does it show complex roots?

Yes. When D < 0, conjugate complex roots are shown as a ± bi.

What if a is 0?

It solves the linear equation and labels it as such. If a = b = 0, you get an identity or no solution.

Is my input sent anywhere?

No. All calculation runs in your browser; nothing is sent to toco.tools servers.