Question

Wie löst man 0=k^{2} *x^{3}+6kx^{2}+9x?

Answer 1

k² • x³ + 6k • x² + 9x = 0

k² • x ausklammern:

k² • x • ( x² + 6/k +  9/k² • x )  = 0   

Nullproduktsatz  →  x = 0  oder  x² + 6/k • x + 9/k² = 0

x² + 6/k • x + 9/k = 0 

x² + px + q = 0

pq-Formel:  p = 6/k  ; q = 9/k²

x_1,2 = - p/2 ± \(\sqrt{(p/2)^2 - q}\)

x_1,2 = - 3/k ± \(\sqrt[]{9/k^2 - 9/k^2}\)

x_1,2 = - 3/k   (dopppelte Nullstelle)

L = { 0 ; - 3/k }

Gruß Wolfgang