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

Quadratische Gleichung

x^2+p x=q

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

Variiere an P und A

Ha Jan 05

p und q positiv

q':=\sqrt {q}

p':=\frac{p}{2}

A = Point(yAxis)
P = Point(xAxis)
C = Midpoint((0, 0), P)
z = Segment(A, C)
b = OrthogonalLine(A, z)
c = OrthogonalLine(C, z)
d = Circle(C, A)
e = Circle(A, C)
D, E = Intersect(d, c)
F, G = Intersect(e, b)
R, c_1, d_1, g, a_1 = Polygon(C, D, G, A)
O = (0, 0)
f = Circle(C, O)
K, L = Intersect(f, c)
h = Line(A, C)
M, N = Intersect(f, h)
i = OrthogonalLine(M, z)
j = OrthogonalLine(K, c_1)
H = Intersect(g, j)
I = Intersect(j, i)
J = Intersect(d_1, i)
Q, i_1, j_1, g_1, k = Polygon(I, J, G, H)
p' = Segment(O, C)
q' = Segment(A, O)
T4: "Lösung ist k = " + k
A1: (-y(A), y(A))
A2: (-y(A), 0)
S, a2, o, a, a1 = Polygon(A2, O, A, A1)
C1: (0, -x(C))
C2: (x(C), -x(C))
T, o_1, c_2, c2, c1 = Polygon(O, C, C2, C1)
U, m, c_3, k_1, i_2 = Polygon(M, C, K, I)
T10: "p=" + (x(P))
T11: "q=" + (y(A)²)