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116962,1374*x-15799,9229=-406,8832*x^3+1522,1581*x^2-3397,7295*x+5949,6816 la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
                                         3              2                          
116962.1374*x - 15799.9229 = - 406.8832*x  + 1522.1581*x  - 3397.7295*x + 5949.6816
116962.1374x15799.9229=(3397.7295x+(406.8832x3+1522.1581x2))+5949.6816116962.1374 x - 15799.9229 = \left(- 3397.7295 x + \left(- 406.8832 x^{3} + 1522.1581 x^{2}\right)\right) + 5949.6816
Teorema de Cardano-Vieta
reescribamos la ecuación
116962.1374x15799.9229=(3397.7295x+(406.8832x3+1522.1581x2))+5949.6816116962.1374 x - 15799.9229 = \left(- 3397.7295 x + \left(- 406.8832 x^{3} + 1522.1581 x^{2}\right)\right) + 5949.6816
de
ax3+bx2+cx+d=0a x^{3} + b x^{2} + c x + d = 0
como ecuación cúbica reducida
x3+bx2a+cxa+da=0x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0
1x33.74101978159826x2+295.809379448451x53.4541718606224=01 x^{3} - 3.74101978159826 x^{2} + 295.809379448451 x - 53.4541718606224 = 0
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=3.74101978159826p = -3.74101978159826
q=caq = \frac{c}{a}
q=295.809379448451q = 295.809379448451
v=dav = \frac{d}{a}
v=53.4541718606224v = -53.4541718606224
Fórmulas de Cardano-Vieta
x1+x2+x3=px_{1} + x_{2} + x_{3} = - p
x1x2+x1x3+x2x3=qx_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q
x1x2x3=vx_{1} x_{2} x_{3} = v
x1+x2+x3=3.74101978159826x_{1} + x_{2} + x_{3} = 3.74101978159826
x1x2+x1x3+x2x3=295.809379448451x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = 295.809379448451
x1x2x3=53.4541718606224x_{1} x_{2} x_{3} = -53.4541718606224
Gráfica
02468-8-6-4-210-25000002500000
Suma y producto de raíces [src]
suma
0.181099486269204 + 1.77996014766453 - 17.0879027848514*I + 1.77996014766453 + 17.0879027848514*I
(0.181099486269204+(1.7799601476645317.0879027848514i))+(1.77996014766453+17.0879027848514i)\left(0.181099486269204 + \left(1.77996014766453 - 17.0879027848514 i\right)\right) + \left(1.77996014766453 + 17.0879027848514 i\right)
=
3.74101978159826
3.741019781598263.74101978159826
producto
0.181099486269204*(1.77996014766453 - 17.0879027848514*I)*(1.77996014766453 + 17.0879027848514*I)
0.181099486269204(1.7799601476645317.0879027848514i)(1.77996014766453+17.0879027848514i)0.181099486269204 \left(1.77996014766453 - 17.0879027848514 i\right) \left(1.77996014766453 + 17.0879027848514 i\right)
=
53.4541718606224
53.454171860622453.4541718606224
53.4541718606224
Respuesta rápida [src]
x1 = 0.181099486269204
x1=0.181099486269204x_{1} = 0.181099486269204
x2 = 1.77996014766453 - 17.0879027848514*I
x2=1.7799601476645317.0879027848514ix_{2} = 1.77996014766453 - 17.0879027848514 i
x3 = 1.77996014766453 + 17.0879027848514*I
x3=1.77996014766453+17.0879027848514ix_{3} = 1.77996014766453 + 17.0879027848514 i
x3 = 1.77996014766453 + 17.0879027848514*i
Respuesta numérica [src]
x1 = 1.77996014766453 + 17.0879027848514*i
x2 = 1.77996014766453 - 17.0879027848514*i
x3 = 0.181099486269204
x3 = 0.181099486269204