Mathe Helferlein
Mathematik (endlich) verstehen
Quadratische Gleichungen
Übersicht Online Rechner Übungsaufgaben ABC-Formel ABC-Formel Rechner ABC-Formel Übungsaufgaben PQ-Formel PQ-Formel Rechner PQ-Formel Übungsaufgaben

Binomische Formeln
Binomische Formeln Rechner Übungsaufgaben

Quadratische Gleichungen Rechner Online

Online Rechner für Quadratische Gleichungen. Der Rechner formt Gleichungen, welche nicht in der Nullform liegen, erst in die Nullform um. Abhängig davon ob die resultierende Gleichung der ABC Form oder der PQ Form entspricht wird sie anschließend mit Hilfe der dafür geeigneten Formel gelöst. Auch die beiden Spezialfälle ohne linearem bzw. absolutem Glied werden bei der Berechnung speziell berücksichtigt.

Beispiele für Quadratische Gleichungen
$x^2 + 6x + 8$
$x^2 - \frac{2}{3} - 5 = 0$
$-(3x+3)(2x+4)$
$12 x^2 + 1 = 7x$
$\sqrt{3} x^2 + \sqrt{3} = 6x$

Weitere Beispiele findest Du in den Quadratische Gleichungen Übungsaufgaben


Wie lautet Deine Quadratische Gleichung?

Folgendes wird berechnet:



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Deine eingegebene Formel

${\left(x-3\right)}^{2} = 4$

Klammern ausrechnen, vereinfachen, umschreiben

$x^{2}-6x+9 = 4$


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Alle Werte der rechten Seite auf die linke Seite bringen (Nullform)

$x^{2}-6x+9-4 = 0$


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Und das Ganze zusammenfassen

$x^{2}-6x+5 = 0$

$a = 1$ - Berechne die quadratische Gleichung mit der PQ Formel


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Die PQ-Formel zum Berechnen

$x^2-6x+5 = 0$

mit den Werten

$p = -6$ und $q = 5$

einsetzen in die PQ Formel

$x_{1,2}=-{\frac{p}{2} \pm \sqrt{\left(\frac{p}{2}\right)^2-q}}$

Einsetzen in die PQ-Formel liefert

$x_{1,2}=-\frac{-6}{2} \pm \sqrt{\left(\frac{-6}2\right)^2-5}$

Nach Möglichkeit $-\frac{p}{2}$ vereinfachen, Quadrat in der Wurzel ausrechnen

$x_{1,2}=3 \pm \sqrt{9-5}$

Wert in der Wurzel ausrechnen

$x_{1,2}=3\pm \sqrt{4}$

Wurzel ziehen

$x_{1,2}=3\pm 2$

Als Ergebnis erhält man

$x_{1}=5$

$x_{2}=1$