Mathematik
Sofort, privat und kostenlos
Quadratische Gleichungen losen.
Losen Sie quadratische Gleichungen ax² + bx + c = 0
Berechnung auf dem GerätKeine Anmeldung
01
Werte eingeben
Ergebnisse werden während der Eingabe aktualisiert.
02 / ANTWORT
Losen: ax² + bx + c = 0
1x² -5x + 6 = 0
Diskriminantenanalyse
Diskriminante (Δ)1.0000
Art der Nullstellen✓ Zwei verschiedene reelle Nullstellen
Losung x₁
3.0000
Losung x₂
2.0000
Parabel-Eigenschaften
Scheitelpunkt(2.5000, -0.2500)
Symmetrieachsex = 2.5000
Y-Achsenabschnitt(0, 6)
Offnung↑ Nach oben (Minimum)
Quadratische Gleichungen verstehen
Quadratische Formel: x = (-b ± √(b² - 4ac)) / 2a. Diese Formel lost jede quadratische Gleichung ax² + bx + c = 0.
Diskriminante (Δ): Der Wert Δ = b² - 4ac bestimmt die Art der Nullstellen:
- • Δ > 0: Zwei verschiedene reelle Nullstellen (Parabel schneidet x-Achse zweimal)
- • Δ = 0: Eine doppelte reelle Nullstelle (Parabel beruhrt x-Achse einmal)
- • Δ < 0: Zwei komplexe Nullstellen (Parabel beruhrt x-Achse nicht)
Scheitelpunktform: Der Scheitelpunkt ist der Minimum- (a > 0) oder Maximum-Punkt (a < 0) der Parabel. Er liegt bei x = -b/(2a).
Cite this calculator
Canonical URL: https://mathify.one/de/math/quadratic
Cite as: Mathify. (2026). Quadratische Gleichungen losen. https://mathify.one/de/math/quadratic
Use Cases
Homework and Exam Preparation
Quickly verify your manual solutions to quadratic equations, check your work, and understand the step-by-step process.
Example: Solve x² - 5x + 6 = 0 to get roots 2 and 3.
Engineering and Physics Calculations
Find roots of quadratic equations that arise in projectile motion, circuit analysis, and optimization problems.
Example: Determine the time when a projectile hits the ground using h = -4.9t² + 20t + 1.
Frequently Asked Questions
- How do I use the Quadratic Solver?
- Enter the coefficients a, b, and c from your quadratic equation ax² + bx + c = 0. The solver will compute the roots using the quadratic formula and display the solutions, including complex roots if the discriminant is negative.
- What if the discriminant is negative?
- If the discriminant (b² - 4ac) is negative, the equation has no real roots. The solver will show the complex roots in the form of a + bi, where i is the imaginary unit.
- Can the solver handle a = 0?
- If a = 0, the equation is not quadratic but linear. The solver will indicate that the equation is not quadratic and may not provide a solution. Ensure a ≠ 0 for a valid quadratic equation.
Tips & Common Mistakes
Tips
- Ensure the equation is in standard form ax² + bx + c = 0 before entering coefficients.
- Double-check the signs of b and c; a common error is entering a negative b as positive.
- Use the discriminant (b² - 4ac) to predict the nature of roots: positive for two real, zero for one real, negative for complex.
- If a = 0, the equation is linear, not quadratic, so the solver may not work correctly.
Common Mistakes to Avoid
- Entering coefficients in the wrong order (e.g., swapping a and c).
- Forgetting to include the sign of the coefficient (e.g., entering 5 instead of -5 for b).
- Assuming the solver can handle a = 0; it's designed for quadratic equations only.
Last updated: August 13, 2026