ΛΥΣΗ ΑΝΙΣΩΣΗΣ Β' ΒΑΘΜΟΥ (QUATRATIC INEQUALITY)
Author: Loizos

Γραφική παράσταση συνάρτησης

Ρίζες της εξίσωσης f(x)=0

Θετικές λύσεις

Αρνητικές λύσεις

Λύσεις

\fgcolor{009999}{ f( } \fgcolor{009999}{ x } \fgcolor{009999}{ ) } \,=\, \fgcolor{009999}{α} \fgcolor{990099}{ x }²  \,+\,  \fgcolor{009999}{β}  \fgcolor{990099}{ x } \,+\, \fgcolor{009999}{γ}

discriminant \,=\, \fgcolor{0000bb}{x}^2  \,-\, 4  \, \fgcolor{ff0000}{a} \, \fgcolor{009999}{c}

Λύσεις της αντίστοιχης ανίσωσης

a = 10 (slider from -10 to 10, step 1)
β = -2 (slider from -10 to 10, step 1)
γ = -9 (slider from -20 to 20, step 1)
f(x) = (a * x^(2)) + (β * x) + γ
d: β^(2) - ((4 * a) * γ)
Root1: ((-β) + sqrt(d)) / ((2 * a))
Root2: ((-β) - sqrt(d)) / ((2 * a))
X_2 = If(Root1 < Root2, (Root1, 0), (Root2, 0))
X_1 = If(Root1 < Root2, (Root2, 0), (Root1, 0))
sgn4ac = If(((4 * a) * γ) < 0, "+", "-")
bsqr: β^(2)
abs4ac: abs(((4 * a) * γ))
showFunction = true
showRoots = true
showPos = false
showNeg = true
showSolution = false
inner = If(Root1 ≠ Root2, Segment[(x(X_1), 0), (x(X_2), 0)])
shadeInner = Integral(f, x(X_2), x(X_1))
outerLeft = Vector(If[Defined[Root2], (x(X_2), 0), (x(Corner[2]), 0)], (x(Corner[1]), 0))
shadeLeft = Integral(f, x(Corner[1]), If[Defined[Root2], x(X_2), x(Corner[2])])
outerRight = Vector((x(X_1), 0), (x(Corner[2]), 0))
shadeRight = Integral(f, x(X_1), x(Corner[2]))
bShow: If[β > 0, "+" + β + "x", If[β < 0, β + "x", ""]] + ""
cShow: If[γ > 0, "+" + γ, If[γ < 0, "" + γ, ""]] + ""
aCoef: If[a ≠ 0, " \fgcolor{ff0000}{" + (If[abs(a) ≠ 1, Text[a], If[a ≟ 1, "", "-"]]) + "} \fgcolor{990099}{ x }^2 ", ""] + ""
bCoef: If[β ≠ 0, "\fgcolor{0000bb}{" + (If[β > 0, "+", "-"]) + (Text[abs(β)]) + " } \fgcolor{990099}{x}", ""] + ""
cCoef: If[γ ≠ 0, "\fgcolor{999900}{" + (If[γ > 0, "+", "-"]) + (Text[abs(γ)]) + " }", ""] + ""
ftxt: aCoef + bCoef + cCoef + ""
text4 = If(d > 0, "έχει \,\ 2 \,\, λύσεις", If[d < 0, "δεν\,\ έχει \,\ λύση", "έχει \,\ 1 \,\,  λύση \,\ (διπλή \,\ ρίζα)"])
ineq1 = If(a > 0, "≤", "≥")
ineq2 = If(a < 0, "≤", "≥")
w: x(Corner[1]) + (0.6 * x(Corner[2] - Corner[1]))
B: (w, y(Corner[2]))
C: (x(Corner[2]), y(Corner[2]))
D: (x(Corner[2]), y(Corner[3]))
text9: ftxt + ineq2 + "0 \,\,in\,\, (-∞,∞)" + ""
text7: ftxt + ineq1 + "0 \,\,in\,\, [" + (x(X_2)) + "," + (x(X_1)) + "]"
text8: ftxt + ineq2 + "0 \,\,in\,\, (-∞," + (x(X_2)) + "] \,\,,\,\,[" + (x(X_1)) + ",∞)"
text6: "Οι λύσεις είναι:    x_1 = " + (x(X_1)) + " και   x_2 = " + (x(X_2)) + "."
text5: "Η\,\,εξίσωση\:\:" + ftxt + " \,=\, 0\,\, :" + text4 + "."
text2: "\fgcolor{009999}{ f( } \fgcolor{009999}{ x } \fgcolor{009999}{ ) } \,=\, " + (LaTeX[ftxt]) + ""