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Beliebt Algebra >

t^4-5t^3+5t^2+17t-42=0

Lösung

t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 = 0

Lösung

t = - 2, t = 3, t = 2 + 3 i, t = 2 - 3 i

Schritte zur Lösung

t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 = 0

Faktorisiere

t^{4} - 5 t^{3} + 5 t^{2} + 17 t - 42 : (t + 2) (t - 3) (t^{2} - 4 t + 7)

(t + 2) (t - 3) (t^{2} - 4 t + 7) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

t + 2 = 0 or t - 3 = 0 or t^{2} - 4 t + 7 = 0

Löse

t + 2 = 0 : t = - 2

Löse

t - 3 = 0 : t = 3

Löse

t^{2} - 4 t + 7 = 0 : t = 2 + 3 i, t = 2 - 3 i

Die Lösungen sind

t = - 2, t = 3, t = 2 + 3 i, t = 2 - 3 i

Graph

Beliebte Beispiele

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

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

6x^3+x^2-24x-4=0

6 x^{3} + x^{2} - 24 x - 4 = 0

solvefor x,x^3+y^3=27

so l v e f or x, x^{3} + y^{3} = 27

x^{3} + 6 x^{2} - 81 = 0

solvefor x,x^3+y^3=18

so l v e f or x, x^{3} + y^{3} = 18