30x^4-4x^3-36x^2+4x=0

Lösung

30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x = 0

x = 0, x \approx 0.11088 \dots, x \approx - 1.08541 \dots, x \approx 1.10786 \dots

Schritte zur Lösung

30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x = 0

Faktorisiere

30 x^{4} - 4 x^{3} - 36 x^{2} + 4 x : 2 x (15 x^{3} - 2 x^{2} - 18 x + 2)

2 x (15 x^{3} - 2 x^{2} - 18 x + 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x = 0 or 15 x^{3} - 2 x^{2} - 18 x + 2 = 0

Löse

15 x^{3} - 2 x^{2} - 18 x + 2 = 0 : x \approx 0.11088 \dots, x \approx - 1.08541 \dots, x \approx 1.10786 \dots

Die Lösungen sind

x = 0, x \approx 0.11088 \dots, x \approx - 1.08541 \dots, x \approx 1.10786 \dots

4 x^{3} - 13 x^{2} + 4 x - 3 = 0

2 x (100 x^{2} - 9) (x^{2} - 3) = 0

2 x^{4} = 1024 x

2 x^{3} - 1 = x^{6} - 1

x^{3} - 8 i = 0