Disc

A

B

C

Resolución gráfica

Resolución gráfica

Resolución algebraica

Resolución algebraica

Nueva ecuación

Discr= b^2- 4·a·c=

- b ± √(Discr)

2 a

x =                              =   

x =

La ecuación no
tiene solución real.

Ecuación  \; completa

Incompleta \;  (b=0)

Incompleta \;  (c=0)

Cálculo \;  del  \; discriminante

Aplica \;  la  \; fórmula

Soluciones

Despeja  \; x^{2}

Despeja \; x

Saca  \; factor  \; comùn

Resuelve \;  dos  \; ecuaciones

La ecuación no tiene solución.

x=0

D18 = 2
E18 = 2
F18 = 5
J18(x) = (D18 * x^(2)) + (E18 * x) + F18
C17 = 1
B17 = 0
C16 = 0
s = Random(1, 3)
A17 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
E17: ((-A17) * (B17 + C17))
D17: A17
A16 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D16: A16
A15 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D15: A15
A14 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D14: A14
A13 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D13: A13
A12 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D12: A12
A11 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D11: A11
A10 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D10: A10
A9 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D9: A9
A8 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D8: A8
A7 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D7: A7
A6 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D6: A6
A5 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D5: A5
A4 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D4: A4
A3 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D3: A3
A2 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
D2: A2
B16 = -3
E16: ((-A16) * (B16 + C16))
C15 = 4
B15 = 0
E15: ((-A15) * (B15 + C15))
C14 = 1
B14 = 0
E14: ((-A14) * (B14 + C14))
B2 = -1
C2 = 3
E2: ((-A2) * (B2 + C2))
B3 = 1
C3 = 4
E3: ((-A3) * (B3 + C3))
B4 = -3
C4 = 4
E4: ((-A4) * (B4 + C4))
B5 = -3
C5 = -1
E5: ((-A5) * (B5 + C5))
B6 = -2
C6 = -2
E6: ((-A6) * (B6 + C6))
B7 = 2
C7 = 2
E7: ((-A7) * (B7 + C7))
B8 = -1
C8 = -1
E8: ((-A8) * (B8 + C8))
B9 = 4
C9 = 4
E9: ((-A9) * (B9 + C9))
B10 = -3
C10 = 3
E10: ((-A10) * (B10 + C10))
B11 = -1
C11 = 1
E11: ((-A11) * (B11 + C11))
B12 = -4
C12 = 4
E12: ((-A12) * (B12 + C12))
B13 = -2
C13 = 2
E13: ((-A13) * (B13 + C13))
E21 = 2
E20 = 3
E19 = 2
listab: {E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13, E14, E15, E16, E17, E18, E19, E20, E21}
D21 = 4
D20 = 2
D19 = 5
listaa: {D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, D12, D13, D14, D15, D16, D17, D18, D19, D20, D21}
n = Random(1, 20)
a = Element(listaa, n)
b = Element(listab, n)
ba: b / a
M13: C13
L13: B13
M12: C12
L12: B12
M11: C11
L11: B11
M10: C10
L10: B10
M9: C9
L9: B9
M8: C8
L8: B8
M7: C7
L7: B7
M6: C6
L6: B6
M5: C5
L5: B5
M4: C4
L4: B4
M3: C3
L3: B3
M2: C2
L2: B2
F19 = 1
J19(x) = (D19 * x^(2)) + (E19 * x) + F19
F20 = 2
J20(x) = (D20 * x^(2)) + (E20 * x) + F20
F21 = 3
J21(x) = (D21 * x^(2)) + (E21 * x) + F21
L14: B14
M14: C14
L15: B15
M15: C15
L16: B16
M16: C16
J2 = Expand(((A2 * (x - B2)) * (x - C2)))
F2: ((A2 * B2) * C2)
J3 = Expand(((A3 * (x - B3)) * (x - C3)))
F3: ((A3 * B3) * C3)
J4 = Expand(((A4 * (x - B4)) * (x - C4)))
F4: ((A4 * B4) * C4)
J5 = Expand(((A5 * (x - B5)) * (x - C5)))
F5: ((A5 * B5) * C5)
J6 = Expand(((A6 * (x - B6)) * (x - C6)))
F6: ((A6 * B6) * C6)
J7 = Expand(((A7 * (x - B7)) * (x - C7)))
F7: ((A7 * B7) * C7)
J8 = Expand(((A8 * (x - B8)) * (x - C8)))
F8: ((A8 * B8) * C8)
J9 = Expand(((A9 * (x - B9)) * (x - C9)))
F9: ((A9 * B9) * C9)
J10 = Expand(((A10 * (x - B10)) * (x - C10)))
F10: ((A10 * B10) * C10)
J11 = Expand(((A11 * (x - B11)) * (x - C11)))
F11: ((A11 * B11) * C11)
J12 = Expand(((A12 * (x - B12)) * (x - C12)))
F12: ((A12 * B12) * C12)
J13 = Expand(((A13 * (x - B13)) * (x - C13)))
F13: ((A13 * B13) * C13)
J14 = Expand(((A14 * (x - B14)) * (x - C14)))
F14: ((A14 * B14) * C14)
J15 = Expand(((A15 * (x - B15)) * (x - C15)))
F15: ((A15 * B15) * C15)
J16 = Expand(((A16 * (x - B16)) * (x - C16)))
F16: ((A16 * B16) * C16)
L17: B17
listad: {L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15, L16, L17}
r1 = Element(listad, n)
J17 = Expand(((A17 * (x - B17)) * (x - C17)))
M17: C17
listae: {M2, M3, M4, M5, M6, M7, M8, M9, M10, M11, M12, M13, M14, M15, M16, M17}
r2 = Element(listae, n)
F17: ((A17 * B17) * C17)
listac: {F2, F3, F4, F5, F6, F7, F8, F9, F10, F11, F12, F13, F14, F15, F16, F17, F18, F19, F20, F21}
c = Element(listac, n)
listaf: {J2, J3, J4, J5, J6, J7, J8, J9, J10, J11, J12, J13, J14, J15, J16, J17, J18, J19, J20, J21}
ec = Element(listaf, n)
d: y = (a * x^(2)) + (b * x) + c
G2: E2^(2) - ((4 * D2) * F2)
G3: E3^(2) - ((4 * D3) * F3)
G4: E4^(2) - ((4 * D4) * F4)
G5: E5^(2) - ((4 * D5) * F5)
G6: E6^(2) - ((4 * D6) * F6)
G7: E7^(2) - ((4 * D7) * F7)
G8: E8^(2) - ((4 * D8) * F8)
G9: E9^(2) - ((4 * D9) * F9)
G10: E10^(2) - ((4 * D10) * F10)
G11: E11^(2) - ((4 * D11) * F11)
G12: E12^(2) - ((4 * D12) * F12)
G13: E13^(2) - ((4 * D13) * F13)
G14: E14^(2) - ((4 * D14) * F14)
G15: E15^(2) - ((4 * D15) * F15)
G16: E16^(2) - ((4 * D16) * F16)
G17: E17^(2) - ((4 * D17) * F17)
G19: E19^(2) - ((4 * D19) * F19)
G20: E20^(2) - ((4 * D20) * F20)
H14 = If(G14 ≥ 0, sqrt(G14), 1000)
H15 = If(G15 ≥ 0, sqrt(G15), 1000)
H16 = If(G16 ≥ 0, sqrt(G16), 1000)
H17 = If(G17 ≥ 0, sqrt(G17), 1000)
H19 = If(G19 ≥ 0, sqrt(G19), 1000)
H20 = If(G20 ≥ 0, sqrt(G20), 1000)
H2 = If(G2 ≥ 0, sqrt(G2), 1000)
H3 = If(G3 ≥ 0, sqrt(G3), 1000)
H4 = If(G4 ≥ 0, sqrt(G4), 1000)
H5 = If(G5 ≥ 0, sqrt(G5), 1000)
H6 = If(G6 ≥ 0, sqrt(G6), 1000)
H7 = If(G7 ≥ 0, sqrt(G7), 1000)
H8 = If(G8 ≥ 0, sqrt(G8), 1000)
H9 = If(G9 ≥ 0, sqrt(G9), 1000)
H10 = If(G10 ≥ 0, sqrt(G10), 1000)
H11 = If(G11 ≥ 0, sqrt(G11), 1000)
H12 = If(G12 ≥ 0, sqrt(G12), 1000)
H13 = If(G13 ≥ 0, sqrt(G13), 1000)
G21: E21^(2) - ((4 * D21) * F21)
H21 = If(G21 ≥ 0, sqrt(G21), 1000)
e = -5 (slider from -5 to 10, step 0.001)
v = 0 (slider from -5 to 5, step 0.1)
A: (e, 0)
f = OrthogonalLine(A, xAxis)
B = Intersect(d, f, 1)
g = Segment(A, B)
C = Intersect(d, xAxis, 1)
D = Intersect(d, xAxis, 1)
E = Intersect(d, xAxis, 2)
rg = 0 (slider from 0 to 1, step 1)
ra = 1 (slider from 0 to 1, step 1)
texto1a: "" + (LaTeX[a]) + " x^2 +" + (LaTeX[b]) + "x+" + (LaTeX[c]) + "=0"
texto1b: "" + (LaTeX[a]) + "  x^2 +" + (LaTeX[b]) + " x+ =0"
texto1c: "" + (LaTeX[a]) + "  x^2 + " + (LaTeX[c]) + " =0"
texto1 = If(b ≟ 0, texto1c, If[c ≟ 0, texto1b, texto1a])
texto2: "" + (LaTeX[d]) + ""
B18 = NaN
B19 = NaN
B20 = NaN
C18 = NaN
lista5: {L2, L3, L4, L5, L6, L7, L8, L9, L10, L11, L12, L13, L14, L15, L16, L17, L18}
lista6: {M2, M3, M4, M5, M10, M11, M12, M13, M14, M15, M16, M17}
texto2b: "" + (LaTeX[a]) + " x^2+" + (LaTeX[b]) + "x+" + (LaTeX[c]) + ""
C19 = NaN
C20 = NaN
C21 = NaN
texto3b: "La ecuación " + ec + " = 0  tiene una solución real
porque la parábola " + d + " solo  tiene
un punto de corte con el eje de abscisas en  x = " + r1 + ""
texto3a: "La ecuación " + ec + " = 0 tiene dos soluciones reales
porque la parábola " + d + " tiene
dos puntos de corte con el eje de abscisas
en  x = " + r1 + "   y   x = " + r2 + ""
texto3c: "La ecuación " + ec + " = 0 no tiene solución real
porque la parábola " + d + " no  tiene
ningún punto de corte con el eje de abscisas."
F = (-4.628011209990657, -11.255618800687309)
texto3 = If(n ≥ 18, texto3c, If[(n ≥ 5) ∧ (n ≤ 8), texto3b, texto3a])
A18 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
A19 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
A20 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
A21 = If(s ≥ 2, Random[1, 5], (Random[1, 5] * (-1)))
B21 = NaN
di: b^(2) - ((4 * a) * c)
texto4a: "= " + (LaTeX[b]) + "^2- 4·\left( " + (LaTeX[a]) + "  \right)·\left(  " + (LaTeX[c]) + " \right)  =" + (LaTeX[di]) + ""
bm: (-ba)
a2: (2 * a)
texto4g: "" + a2 + ""
dir: sqrt(di)
texto4i: "" + a2 + ""
texto4j: "x \space = \space " + (LaTeX[r1]) + ""
texto4k: " x \space = \space " + (LaTeX[r2]) + ""
G = (-2.8618341619318213, 5.001383698624664)
H = (0.22499112215909237, 5.018251596351936)
h = Segment(G, H)
I = (1, 5)
J = (4.526305042613644, 5.018251596351936)
i = Segment(I, J)
K = (-2, 3)
L = (0.4948774857954564, 3.0278396645337606)
j = Segment(K, L)
M = (1, 3)
N = (1.9792524857954532, 3.6350839827155896)
u = Vector(M, N)
O = (1.9792524857954532, 2.454331141806499)
w = If(c ≟ 0, 2, If[b ≟ 0, 3, 1])
k = Vector(M, O)
cm: (-c)
texto4: "" + (LaTeX[a]) + "·x^2 =" + (LaTeX[cm]) + ""
c2: cm / a
texto5b: "x=±√ \left(  " + (LaTeX[c2]) + " \right) "
texto6b: "" + (LaTeX[a]) + "x \space (x \space +\space " + (LaTeX[ba]) + ") \space = \space 0"
G18: E18^(2) - ((4 * D18) * F18)
H18 = If(G18 ≥ 0, sqrt(G18), 1000)
texto6a: "" + (LaTeX[a]) + "x \space (x  \space  \space " + (LaTeX[ba]) + ") \space = \space 0"
texto6e = If(ba ≥ 0, texto6b, texto6a)
texto6aa: " x \space (x \space  " + (LaTeX[ba]) + ") \space = \space 0"
texto6bb: " x \space (x \space  \space " + (LaTeX[bm]) + " ) \space = \space 0"
texto6ee = If(ba ≥ 0, texto6bb, texto6aa)
texto6 = If(a ≟ 1 ∨ a ≟ -1, texto6ee, texto6e)
P = (-2.8618341619318213, 3.297726028170125)
Q = (1.1864612926136398, 1.341049891806499)
S = (4.172079190340916, 1.7796152327155903)
b2: (-b)
texto4f: "" + (LaTeX[b2]) + "±√\left( " + (LaTeX[di]) + "  \right) "
texto4h: "" + (LaTeX[b2]) + " \space ± \space " + (LaTeX[dir]) + ""
vx: ((-b)) / ((2 * a))
vy: (a * vx^(2)) + (b * vx) + c
texto7b: "El vértice de la parábola está en ( " + vx + " , " + vy + " )
Las ramas van hacia abajo."
texto7a: "El vértice de la parábola está en ( " + vx + " , " + vy + " )
Las ramas van hacia arriba"
texto7 = If(a ≥ 0, texto7a, texto7b)
R = (-4.5282919280106935, 22.32290690376274)
U = (2.568395238500127, -5.566078560203326)
V = (1.0677506908800376, 13.555037449794613)
W = (4.456302895183465, 13.264590117997177)
Vértice: (vx, vy)
l = 4 (slider from 1 to 4, step 1)
texto5a: "x^2= \frac{" + (LaTeX[cm]) + "}{" + (LaTeX[a]) + "}=" + (LaTeX[c2]) + ""
texto14: "x^2=" + (LaTeX[c2]) + ""
texto5e: "" + (LaTeX[ec]) + " \; = \; 0"
texto5: " " + (LaTeX[ec]) + "  \; =  \; 0"
T1 = (-2.1840354767184036, 5.795375802339314)
T2 = (-2.219512195121951, 4.642382665824326)
T3 = (-2.1662971175166295, 3.347482681738262)
T4 = (-2.2017738359201773, 2.3009196809015804)
texto9: "x" + (LaTeX[ba]) + "=0"
T = (-2.608815696022729, 6.013457562261024)
Z = (0.10120738636363658, 1.113281249999997)
texto11: "x+" + (LaTeX[ba]) + "=0"
texto10: "" + (LaTeX[a]) + " \; x= \; 0"