Quadratische Gleichung interaktiv
Author: Prof. Dr. Haftendorn
Date: 31.01.05

p udn q wählen

Quadratische Gleichung

x^2+p x=q

x^2+2 p' x=q'^{  2}

Ha Jan 05

p und q positiv

q':=\sqrt {q}=a_q

x_2 negativ nehnen

O = (0, 0)
p = 10 (slider from 0 to 22, step 0.1)
P: (p, 0)
C = Midpoint((0, 0), P)
f = Circle(C, O)
q = 64 (slider from 0 to 256, step 0.1)
q': sqrt(q)
A: (0, q')
h = Line(A, C)
M, N = Intersect(f, h)
d = Circle(C, A)
z = Segment(A, C)
i = OrthogonalLine(M, z)
c = OrthogonalLine(C, z)
K, L = Intersect(f, c)
D, E = Intersect(d, c)
b = OrthogonalLine(A, z)
e = Circle(A, C)
p' = Segment(O, C)
A1: (-q', q')
A2: (-q', 0)
C1: (0, -p / 2)
C2: (p / 2, -p / 2)
S, o, c1, c2, c_2 = Polygon(O, C1, C2, C)
T, a_q, a0, a1, a2 = Polygon(O, A, A1, A2)
B, F = Intersect(e, b)
Q, a_1, c_1, d_1, f_1 = Polygon(A, C, D, F)
g = OrthogonalLine(K, c_1)
J = Intersect(g, i)
H = Intersect(g, b)
I = Intersect(d_1, i)
R, k, j, i_1, f_2 = Polygon(H, J, I, F)
x_1 = Segment(A, M)
U, m, j_1, k_1, c_3 = Polygon(M, J, K, C)
r = Circle(C, D)
G = Intersect(r, xAxis, 1)
Neg: (x(G), -p')
x_2 = Segment(C1, Neg)
s = CircleArc(C, G, D)
T4: "Lösung ist k=x_1=" + k
T9: "und x_2 = " + (-x(G))