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Beliebt Algebra >

x^4-6x^2-7x-6=0

Lösung

x^{4} - 6 x^{2} - 7 x - 6 = 0

Lösung

x = - 2, x = 3, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Schritte zur Lösung

x^{4} - 6 x^{2} - 7 x - 6 = 0

Faktorisiere

x^{4} - 6 x^{2} - 7 x - 6 : (x + 2) (x - 3) (x^{2} + x + 1)

(x + 2) (x - 3) (x^{2} + x + 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x + 2 = 0 or x - 3 = 0 or x^{2} + x + 1 = 0

Löse

x + 2 = 0 : x = - 2

Löse

x - 3 = 0 : x = 3

Löse

x^{2} + x + 1 = 0 : x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Die Lösungen sind

x = - 2, x = 3, x = - \frac{1}{2} + i \frac{3}{2}, x = - \frac{1}{2} - i \frac{3}{2}

Graph

Beliebte Beispiele

x^4-8x^3+21x^2-20x+5=0

x^{4} - 8 x^{3} + 21 x^{2} - 20 x + 5 = 0

b^{3} - 125 = 0

4x^3-8x^2+5x-73=0

4 x^{3} - 8 x^{2} + 5 x - 73 = 0

x (x - 2) (x + 5) = 0

-9= 5/4 x^{45}x

- 9 = \frac{5}{4} x^{45} x