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Beliebt Algebra >

-4r^5+4r^4+0.25r-0.25=0

Lösung

- 4 r^{5} + 4 r^{4} + 0.25 r - 0.25 = 0

Lösung

r = 1, r = \frac{1}{2} i, r = - \frac{1}{2} i, r = - \frac{1}{2}, r = \frac{1}{2}

Schritte zur Lösung

- 4 r^{5} + 4 r^{4} + 0.25 r - 0.25 = 0

Multipliziere beide Seiten mit

100

- 400 r^{5} + 400 r^{4} + 25 r - 25 = 0

Faktorisiere

- 400 r^{5} + 400 r^{4} + 25 r - 25 : - 25 (r - 1) (4 r^{2} + 1) (2 r + 1) (2 r - 1)

- 25 (r - 1) (4 r^{2} + 1) (2 r + 1) (2 r - 1) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

r - 1 = 0 or 4 r^{2} + 1 = 0 or 2 r + 1 = 0 or 2 r - 1 = 0

Löse

r - 1 = 0 : r = 1

Löse

4 r^{2} + 1 = 0 : r = \frac{1}{2} i, r = - \frac{1}{2} i

Löse

2 r + 1 = 0 : r = - \frac{1}{2}

Löse

2 r - 1 = 0 : r = \frac{1}{2}

Die Lösungen sind

r = 1, r = \frac{1}{2} i, r = - \frac{1}{2} i, r = - \frac{1}{2}, r = \frac{1}{2}

Graph

Beliebte Beispiele

solvefor m,L=12m^3

so l v e f or m, L = 12 m^{3}

-x^3+54x^2-6x+25=0

- x^{3} + 54 x^{2} - 6 x + 25 = 0

\frac{x ^{5}}{3} = 1 0^{6}

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

r^{3} - 3 r^{2} - r + 3 = 0