4x^4+8x^3-17x^2-21x-18=0

Lösung

4 x^{4} + 8 x^{3} - 17 x^{2} - 21 x - 18 = 0

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

Schritte zur Lösung

4 x^{4} + 8 x^{3} - 17 x^{2} - 21 x - 18 = 0

Faktorisiere

4 x^{4} + 8 x^{3} - 17 x^{2} - 21 x - 18 : (x - 2) (x + 3) (4 x^{2} + 4 x + 3)

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

Anwendung des Nullfaktorprinzips: Wenn

ab = 0

dann

a = 0

oder

b = 0

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

Löse

x - 2 = 0 : x = 2

Löse

x + 3 = 0 : x = - 3

Löse

4 x^{2} + 4 x + 3 = 0 : x = - \frac{1}{2} + i \frac{2}{2}, x = - \frac{1}{2} - i \frac{2}{2}

Die Lösungen sind

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

x^{8} + 16 = 17 x^{4}

y^{3} + 5 y^{2} - 36 y - 180 = 0

x^{4} + 49 x^{2} = 0

(x - 1) (x + 2)^{2} (x^{2} - 6 x + 10) = 0

3 y (3 y - 5) (2 y + 7) = 0