Kubische Gleichung mit Quasikonstruktion
Author: Prof. Dr. Dörte Haftendorn Prof. Dr. Riebesehl
Date: Feb 2006

Lösung der Gleichung

bei Vorgabe einer Einheitsparabel

x^3+px+q=0

Riebesehl 06

Ha 06

p = -3.25 (slider from -5 to 4, step 0.0010)
q = 1.5 (slider from -5 to 5, step 0.0010)
Q': (-q, 0)
B = Point(xAxis)
M_q = Midpoint(Q', B)
P': (0, -p)
E = (0, 1)
M_p = Midpoint(E, P')
a = OrthogonalLine(M_q, xAxis)
c = OrthogonalLine(M_p, yAxis)
M = Intersect(c, a)
d = Circle(M, B)
H, I, J, K = Intersect(d, Einheitsparabel)
b = OrthogonalLine(H, xAxis)
e = OrthogonalLine(J, xAxis)
f(x) = x^(3) + p * x + q
H_x = Intersect(b, xAxis)
M_1, M_2, M_3 = Intersect(f, xAxis)
J_x = Intersect(e, xAxis)
x_1: x(H_x)
x_3: x(J_x)
g = OrthogonalLine(K, xAxis)
K_x = Intersect(g, xAxis)
x_2: x(K_x)
Text2: "" + f