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(-0.06x^3)-1.06x^2+4.26x+11.43005=0 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
     3       2                       
  3*x    53*x    213*x               
- ---- - ----- + ----- + 11.43005 = 0
   50      50      50
(213x50+(−3x350−53x250))+11.43005=0\left(\frac{213 x}{50} + \left(- \frac{3 x^{3}}{50} - \frac{53 x^{2}}{50}\right)\right) + 11.43005 = 0
Simplificar
Teorema de Cardano-Vieta
reescribamos la ecuación
(213x50+(−3x350−53x250))+11.43005=0\left(\frac{213 x}{50} + \left(- \frac{3 x^{3}}{50} - \frac{53 x^{2}}{50}\right)\right) + 11.43005 = 0
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
x3+53x23−71x−190.500833333333=0x^{3} + \frac{53 x^{2}}{3} - 71 x - 190.500833333333 = 0
px2+qx+v+x3=0p x^{2} + q x + v + x^{3} = 0
donde
p=bap = \frac{b}{a}
p=533p = \frac{53}{3}
q=caq = \frac{c}{a}
q=−71q = -71
v=dav = \frac{d}{a}
v=−190.500833333333v = -190.500833333333
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=−533x_{1} + x_{2} + x_{3} = - \frac{53}{3}
x1x2+x1x3+x2x3=−71x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = -71
x1x2x3=−190.500833333333x_{1} x_{2} x_{3} = -190.500833333333
Suma y producto de raíces [src] 
suma
-20.6572839731916 + 0.e-20*I + -1.88964585344728 + 0.e-22*I + 4.88026315997222 - 0.e-22*I
(4.88026315997222−2.0⋅10−22i)+((−1.88964585344728+2.0⋅10−22i)+(−20.6572839731916+1.0⋅10−20i))\left(4.88026315997222 - 2.0 \cdot 10^{-22} i\right) + \left(\left(-1.88964585344728 + 2.0 \cdot 10^{-22} i\right) + \left(-20.6572839731916 + 1.0 \cdot 10^{-20} i\right)\right) 
=
-17.6666666666667 + 0.e-20*I
−17.6666666666667+1.0⋅10−20i-17.6666666666667 + 1.0 \cdot 10^{-20} i 
producto
(-20.6572839731916 + 0.e-20*I)*(-1.88964585344728 + 0.e-22*I)*(4.88026315997222 - 0.e-22*I)
(−20.6572839731916+1.0⋅10−20i)(−1.88964585344728+2.0⋅10−22i)(4.88026315997222−2.0⋅10−22i)\left(-20.6572839731916 + 1.0 \cdot 10^{-20} i\right) \left(-1.88964585344728 + 2.0 \cdot 10^{-22} i\right) \left(4.88026315997222 - 2.0 \cdot 10^{-22} i\right) 
=
190.500833333333 - 1.54594937607112e-19*I
190.500833333333−1.54594937607112⋅10−19i190.500833333333 - 1.54594937607112 \cdot 10^{-19} i 
190.500833333333 - 1.54594937607112e-19*i
Respuesta rápida [src] 
x1 = -20.6572839731916 + 0.e-20*I
x1=−20.6572839731916+1.0⋅10−20ix_{1} = -20.6572839731916 + 1.0 \cdot 10^{-20} i 
x2 = -1.88964585344728 + 0.e-22*I
x2=−1.88964585344728+2.0⋅10−22ix_{2} = -1.88964585344728 + 2.0 \cdot 10^{-22} i 
x3 = 4.88026315997222 - 0.e-22*I
x3=4.88026315997222−2.0⋅10−22ix_{3} = 4.88026315997222 - 2.0 \cdot 10^{-22} i 
x3 = 4.88026315997222 - 0.e-22*i
Respuesta numérica [src] 
x1 = -1.88964585344728
x2 = -20.6572839731916
x3 = 4.88026315997222
x3 = 4.88026315997222
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