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Beliebt Algebra >

r^4+r^3-7r^2-r+6=0

Lösung

r^{4} + r^{3} - 7 r^{2} - r + 6 = 0

Lösung

r = - 1, r = 1, r = 2, r = - 3

Schritte zur Lösung

r^{4} + r^{3} - 7 r^{2} - r + 6 = 0

Faktorisiere

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

(r + 1) (r - 1) (r - 2) (r + 3) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

r + 1 = 0 or r - 1 = 0 or r - 2 = 0 or r + 3 = 0

Löse

r + 1 = 0 : r = - 1

Löse

r - 1 = 0 : r = 1

Löse

r - 2 = 0 : r = 2

Löse

r + 3 = 0 : r = - 3

Die Lösungen sind

r = - 1, r = 1, r = 2, r = - 3

Graph

Beliebte Beispiele

4 x - 4 x^{9} = 0

solvefor y,(x^2+y^2)^2=x^2-y^2

so l v e f or y, (x^{2} + y^{2})^{2} = x^{2} - y^{2}

wurzeln von x^3-x^2-x+1=0

roo t s x^{3} - x^{2} - x + 1 = 0

3x^5-8x^4+2x^3+5x^2-2x+1=0

3 x^{5} - 8 x^{4} + 2 x^{3} + 5 x^{2} - 2 x + 1 = 0

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