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Beliebt Algebra >

x^4-2x^3+x-2=0

Lösung

x^{4} - 2 x^{3} + x - 2 = 0

Lösung

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

Schritte zur Lösung

x^{4} - 2 x^{3} + x - 2 = 0

Faktorisiere

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

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x + 1 = 0 : x = - 1

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

Graph

Beliebte Beispiele

(2x+1)(2x+3)(2x+5)(2x+7)=9

(2 x + 1) (2 x + 3) (2 x + 5) (2 x + 7) = 9

(x^3)/3-x^2+x+1=0

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

solvefor x,0=x^4-8x^2-9

so l v e f or x, 0 = x^{4} - 8 x^{2} - 9

43 = a^{3}

x^{8} + 4 x^{2} + 4 = 0