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Beliebt Algebra >

x^4-4x^3+8x^2-16x+16=0

Lösung

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

Lösung

x = 2, x = 2 i, x = - 2 i

Schritte zur Lösung

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 = 0

Faktorisiere

x^{4} - 4 x^{3} + 8 x^{2} - 16 x + 16 : (x - 2)^{2} (x^{2} + 4)

(x - 2)^{2} (x^{2} + 4) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x^{2} + 4 = 0 : x = 2 i, x = - 2 i

Die Lösungen sind

x = 2, x = 2 i, x = - 2 i

Graph

Beliebte Beispiele

3x^4-2x^3+2x^2-8x-40=0

3 x^{4} - 2 x^{3} + 2 x^{2} - 8 x - 40 = 0

solvefor x,x^{1000}+y^{1000}=5

so l v e f or x, x^{1000} + y^{1000} = 5

z^4+2z^3-2z-1=0

z^{4} + 2 z^{3} - 2 z - 1 = 0

4x^4-25x^2+36=0

4 x^{4} - 25 x^{2} + 36 = 0

x^3+3x^2+4x+12=0

x^{3} + 3 x^{2} + 4 x + 12 = 0