coefficient de x²

A jouter des termes en x²

coefficient de x²

\fgcolor{00CC00}{a\, x\, +\, b\,} = \fgcolor{FF0000}{\,c\, x\, +\, d}

S = Ø

S = ℝ

\fgcolor{00CC00}{a\, x²\, +\, b\, x\, +\, c\,} = \fgcolor{FF0000}{\,d\, x²\, +\, e\, x\, +\, f}

Ensemble des solutions:

=

(l'ensemble des nombres réels)

(l'ensemble vide)

d = 1 (slider from -2 to 2, step 1)
f = -3 (slider from -5 to 9, step 1)
e = 1 (slider from -3 to 4, step 1)
quad = false
coeff_2 = If(quad, d, 0)
a = 1 (slider from -2 to 2, step 1)
coeff_1 = If(quad, a, 0)
c = 2 (slider from -5 to 9, step 1)
b = 0 (slider from -3 to 4, step 1)
f_1(x) = coeff_1 * x * x + b * x + c
g(x) = coeff_2 * x * x + e * x + f
A, B = Intersect(f_1, g)
e_1 = Segment(A, (x(A), 0))
h = Segment(B, (x(B), 0))
sol = RemoveUndefined({x(A), x(B)})
b': abs(b)
sgn_f: If[f > 0, "+", If[f < 0, "-", ""]] + ""
sgn_c: If[c > 0, "+", If[c < 0, "-", ""]] + ""
sgn_e: If[e > 0, "+", If[e < 0, "-", ""]] + ""
sgn_b: If[b > 0, "+", If[b < 0, "-", ""]] + ""
a' = If(quad, a, 0)
d' = If(quad, d, 0)
C = Point(yAxis)
D = Point(yAxis)
ega = If((¬quad) ∧ b ≟ e ∧ c ≟ f, true, If[quad ∧ a ≟ d ∧ b ≟ e ∧ c ≟ f, true, false])
sgn_A = If(x(A) < 0, "-", "")
nb = IterationList(x + 1, 1, 999)
sgn_B = If(x(B) < 0, "-", "")
nb_A = Sequence(x(A) * Element[nb, i], i, 1, 1000)
nb_{A'} = Sequence(If[Element[nb_A, i] ≟ floor(Element[nb_A, i]), 1, 0], i, 1, 1000)
max_A = Max(nb_{A'})
nb_B = Sequence(x(B) * Element[nb, i], i, 1, 1000)
nb_{B'} = Sequence(If[Element[nb_B, i] ≟ floor(Element[nb_B, i]), 1, 0], i, 1, 1000)
max_B = Max(nb_{B'})
triche_{ab} = If(quad, "b = " + b, "a = " + b)
E = Point(xAxis)
i = OrthogonalLine(E, xAxis)
F: E + (4, 0)
j = OrthogonalLine(F, xAxis)
G = Point(i)
H = Point(i)
K = Point(xAxis)
k = OrthogonalLine(K, xAxis)
L: K + (4, 0)
l = OrthogonalLine(L, xAxis)
I: G + Vector[G, G + (4, 0)] / 5 * (b + 2)
J: H + Vector[H, H + (4, 0)] / 20 * (c + 10)
triche_{de} = If(quad, "e = " + e, "c = " + e)
M: (x(K), y(G))
N: M + Vector[M, M + (4, 0)] / 5 * (e + 2)
triche_{bc} = If(quad, "c = " + c, "b = " + c)
triche_{ef} = If(quad, "f = " + f, "d = " + f)
O: (x(K), y(H))
P: O + Vector[O, O + (4, 0)] / 20 * (f + 10)
equa_v: If[abs(a') ≟ 1, If[a' > 0, "x^2\,", "-\,x^2\,"], If[a' ≟ 0, "", FractionText[a'] + "\,x^2\,"]] + (If[b ≟ 0, "", If[a' ≟ 0, If[abs(b) ≟ 1, If[b > 0, "x", "-\,x"], If[b > 0, FractionText[abs(b)] + "\,x", sgn_b + "\," + (FractionText[abs(b)]) + "\,x"]], If[abs(b) ≟ 1, If[b > 0, "+\;x", "-\;x"], sgn_b + "\," + (FractionText[abs(b)]) + "\,x"]]]) + (If[c ≟ 0, If[b ≟ 0 ∧ a' ≟ 0, "0", ""], If[b ≟ 0 ∧ a' ≟ 0, c + "", "\," + sgn_c + "\," + (FractionText[abs(c)])]])
equa_r: If[abs(d') ≟ 1, If[d' > 0, "x^2\,", "-\,x^2\,"], If[d' ≟ 0, "", FractionText[d'] + "\,x^2\,"]] + (If[e ≟ 0, "", If[d' ≟ 0, If[abs(e) ≟ 1, If[e > 0, "x", "-\,x"], If[e > 0, FractionText[abs(e)] + "\,x", sgn_e + "\," + (FractionText[abs(e)]) + "\,x"]], If[abs(e) ≟ 1, If[e > 0, "+\;x", "-\;x"], sgn_e + "\," + (FractionText[abs(e)]) + "\,x"]]]) + (If[f ≟ 0, If[e ≟ 0 ∧ d' ≟ 0, "0", ""], If[e ≟ 0 ∧ d' ≟ 0, f + "", "\," + sgn_f + "\," + (FractionText[abs(f)])]])
v = Vector((0.1, 0.35))
haut_{rouge} = If(d' ≟ 0 ∧ e ≟ floor(e), true, false)
haut_{vert} = If(a' ≟ 0 ∧ b ≟ floor(b), true, false)
Q = (15.675678425425295, 11.030114420817815)
R: Q - (0, y(D) - y(C))
haut = If(haut_{rouge} ∧ haut_{vert}, true, false)
T = (10.657439571620028, 18.808159550553206)
U = (10.65744, 6.2)
V = (21.15744, 6.2)
W = (21.157439571620028, 18.808159550553206)
poly1, t, u, v_1, w = Polygon(T, U, V, W)
m = Segment(T, W)
n = Segment(W, V)
p = Segment(V, U)
q = Segment(U, T)
solu_{1ou2}: "S\, =\, \left\{" + (If[max_A ≟ 0, x(A) + "", sgn_A + (FractionText[abs(x(A))])]) + (If[Length[sol] ≟ 1, "", If[max_B ≟ 0, "\,;\," + (x(B)), "\,;\," + sgn_B + (FractionText[abs(x(B))])]]) + "\right\}"
texte_{mes}: If[abs(a') ≟ 1, If[a' > 0, "x^2\,", "-\,x^2\,"], If[a' ≟ 0, "", FractionText[a'] + "\,x^2\,"]] + (If[b ≟ 0, "", If[a' ≟ 0, If[abs(b) ≟ 1, If[b > 0, "x", "-\,x"], If[b > 0, FractionText[abs(b)] + "\,x", sgn_b + "\," + (FractionText[abs(b)]) + "\,x"]], If[abs(b) ≟ 1, If[b > 0, "+\;x", "-\;x"], sgn_b + "\," + (FractionText[abs(b)]) + "\,x"]]]) + (If[c ≟ 0, If[b ≟ 0 ∧ a' ≟ 0, "0", ""], If[b ≟ 0 ∧ a' ≟ 0, c + "", "\," + sgn_c + "\," + (FractionText[abs(c)])]])
A_1 = Corner(texte_{mes}, 3)
B_1 = Corner(texte_{mes}, 4)
C_1: Q - (x(A_1) - x(B_1), 0)
D_1: Q + (0.4, 0)
E_1: C_1 + R - Q
F_1: D_1 + R - Q
G_1 = If(haut_{vert}, E_1, C_1)
H_1 = If(haut_{rouge}, F_1, D_1)
I_1 = Intersect(w, m)
K_1 = Intersect(t, q)
M_1 = Intersect(w, m)
N_1 = Intersect(w, m)
O_1 = Intersect(w, m)
P_1 = Intersect(w, m)
Q_1 = Intersect(w, m)
R_1 = Intersect(w, m)
d_v = Line((0, f_1(0)), (1, f_1(1)))
d_r = Line((0, g(0)), (1, g(1)))
point_{cache} = If((x(A) ≥ x(T)) ∧ (x(A) ≤ x(W)) ∧ (y(A) ≥ y(V)) ∧ (y(A) ≤ y(W)), true, false)
point_{dessus} = If((x(A) ≥ x(T)) ∧ (x(A) ≤ x(W)) ∧ (y(A) ≥ y(W)), true, false)