4x^4-4x^3-7x^2-4x+4=0

Lösung

4 x^{4} - 4 x^{3} - 7 x^{2} - 4 x + 4 = 0

x = 2, x = \frac{1}{2}, x = - \frac{3}{4} + i \frac{7}{4}, x = - \frac{3}{4} - i \frac{7}{4}

Schritte zur Lösung

4 x^{4} - 4 x^{3} - 7 x^{2} - 4 x + 4 = 0

Faktorisiere

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

(x - 2) (2 x - 1) (2 x^{2} + 3 x + 2) = 0

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

x - 2 = 0 or 2 x - 1 = 0 or 2 x^{2} + 3 x + 2 = 0

Löse

x - 2 = 0 : x = 2

Löse

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

Löse

2 x^{2} + 3 x + 2 = 0 : x = - \frac{3}{4} + i \frac{7}{4}, x = - \frac{3}{4} - i \frac{7}{4}

Die Lösungen sind

x = 2, x = \frac{1}{2}, x = - \frac{3}{4} + i \frac{7}{4}, x = - \frac{3}{4} - i \frac{7}{4}

x^{3} + 6 x^{2} + 8 x = 0

so l v e f or x, 2 (x^{4} - y^{4}) = 350

(x - 1) (x + 2) - x^{2} (x + 2) = 21

e (x) = (- x + x^{2})^{2} + 4 x^{3}

3 x^{4} - 24 x^{3} + 48 x^{2} + x - 4 = 0