一元二次不等式
Author: 藍邦偉  老師

$ O $

$ 一元二次不等式 $

$ x∈\mathbb{R} $

$ 無解 $

1

$ 顯示答案 $

k = 10 (slider from 1 to 14, step 1)
list: {-5, -4, -3, -2, -1, -0.5, -0.1, 0.1, 0.5, 1, 2, 3, 4, 5}
u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
Q_2: 0.7 * Corner[1] + 0.3 * Corner[2]
Q_3: (x(Q_2), y(Corner[4]))
poly1, q_1, q_2, q_4, q_3 = Polygon(Corner[1], Q_2, Q_3, Corner[4])
a = Element(list, k)
b = 0 (slider from -8 to 8, step 1)
c = 0 (slider from -8 to 8, step 1)
f(x) = a * x^(2) + b * x + c
A, B = Root(f)
D: b^(2) - 4 * a * c
n = 4 (slider from 1 to 4, step 1)
g = Factor(f)
α = Min(x(A), x(B))
β = Max(x(A), x(B))
text2: "$⇒ " + (LaTeX[g]) + " " + (LaTeX[If[n ≟ 1, ">", If[n ≟ 2, "≥", If[n ≟ 3, "<", "≤"]]]]) + "0$"
Step = 2 (slider from 0 to 3, step 1)
t_{Not Equal}: "$ x≠" + (LaTeX[FractionText[(-b) / 2 * a]]) + "$"
Inequality: "$ f(x)=" + (LaTeX[If[abs(a) ≠ 1, FractionText[a], If[a ≟ 1, "", "-"]]]) + "\;x² " + (LaTeX[If[b ≟ 0, "", If[(b > 0) ∧ (b ≠ 1), "+" * abs(b) * "x", If[b ≟ 1, "+x", If[b ≟ -1, "-x", If[(b < 0) ∧ (b ≠ -1), "-" * abs(b) * "x"]]]]]]) + "" + (LaTeX[If[c ≟ 0, "", If[c > 0, "+" * abs(c), If[c < 0, "-" * abs(c)]]]]) + "" + (LaTeX[If[n ≟ 1, ">", If[n ≟ 2, "≥", If[n ≟ 3, "<", "≤"]]]]) + "0$"
t_{equal}: "$ x=" + (LaTeX[FractionText[(-b) / 2 * a]]) + " $"
C = (-13.57986221149297, 3.898273425257762)
text_{32}: "$ ⇒" + (LaTeX[FractionText[α]]) + "" + (LaTeX[If[n ≟ 3 ∨ n ≟ 1, "<", If[n ≟ 4 ∨ n ≟ 2, "≤"]]]) + "x" + (LaTeX[If[n ≟ 3 ∨ n ≟ 1, "<", If[n ≟ 4 ∨ n ≟ 2, "≤"]]]) + "" + (LaTeX[FractionText[β]]) + " $"
text_{31}: "$ ⇒x" + (LaTeX[If[n ≟ 1 ∨ n ≟ 3, "<", If[n ≟ 2 ∨ n ≟ 4, "≤"]]]) + " " + (LaTeX[FractionText[α]]) + "\;或\;x" + (LaTeX[If[n ≟ 1 ∨ n ≟ 3, ">", If[n ≟ 2 ∨ n ≟ 4, "≥"]]]) + "" + (LaTeX[FractionText[β]]) + "$"
d = true