Kostenloser Rechner für die quadratische Formel
Löse quadratische Gleichungen mit der quadratischen Formel. Berechne die Nullstellen von ax² + bx + c = 0.
Coefficient of x²
Coefficient of x
Constant term
Root1
3.000000
Formel
How to Use the Quadratic Formula
Formula
x = (-b ± √(b² - 4ac)) / (2a)
For the equation ax² + bx + c = 0
Discriminant (Δ = b² - 4ac)
Vertex
The vertex of the parabola is at x = -b/(2a), y = f(-b/(2a)).
Lösungsbeispiel
Solve x² - 5x + 6 = 0 (a=1, b=-5, c=6).
- 01Discriminant = (-5)² - 4(1)(6) = 25 - 24 = 1
- 02Since Δ > 0, there are two distinct real roots
- 03x₁ = (5 + √1) / 2 = 6 / 2 = 3
- 04x₂ = (5 - √1) / 2 = 4 / 2 = 2
- 05Vertex: x = 5/2 = 2.5, y = (2.5)² - 5(2.5) + 6 = -0.25
Häufig Gestellte Fragen
What is the quadratic formula?
The quadratic formula x = (-b ± √(b²-4ac)) / (2a) finds the solutions (roots) of any quadratic equation ax² + bx + c = 0.
What does the discriminant tell us?
The discriminant (b²-4ac) tells you the nature of the roots: positive = 2 real roots, zero = 1 repeated root, negative = no real roots (2 complex roots).
What if the discriminant is negative?
If the discriminant is negative, the equation has no real solutions. The roots are complex numbers. This calculator shows the real part when the discriminant is negative.
Lernen