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-x^4-6x^3+8x^2+6x+9=0 la ecuación

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Solución numérica:

Buscar la solución numérica en el intervalo [, ]

Solución

Ha introducido [src] 
   4      3      2              
- x  - 6*x  + 8*x  + 6*x + 9 = 0
(6x+(8x2+(−x4−6x3)))+9=0\left(6 x + \left(8 x^{2} + \left(- x^{4} - 6 x^{3}\right)\right)\right) + 9 = 0
Simplificar
Respuesta rápida [src] 
                ______________        
               /          ___      ___
       3      /  19   9*\/ 5     \/ 5 
x1 = - - +   /   -- + -------  - -----
       2   \/    2       2         2
x1=−32−52+192+952x_{1} = - \frac{3}{2} - \frac{\sqrt{5}}{2} + \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}} 
                ______________        
               /          ___      ___
       3      /  19   9*\/ 5     \/ 5 
x2 = - - -   /   -- + -------  - -----
       2   \/    2       2         2
x2=−192+952−32−52x_{2} = - \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}} - \frac{3}{2} - \frac{\sqrt{5}}{2} 
                          ________________
             ___         /            ___ 
       3   \/ 5         /    19   9*\/ 5  
x3 = - - + ----- - I*  /   - -- + ------- 
       2     2       \/      2       2
x3=−32+52−i−192+952x_{3} = - \frac{3}{2} + \frac{\sqrt{5}}{2} - i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}} 
                          ________________
             ___         /            ___ 
       3   \/ 5         /    19   9*\/ 5  
x4 = - - + ----- + I*  /   - -- + ------- 
       2     2       \/      2       2
x4=−32+52+i−192+952x_{4} = - \frac{3}{2} + \frac{\sqrt{5}}{2} + i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}} 
x4 = -3/2 + sqrt(5)/2 + i*sqrt(-19/2 + 9*sqrt(5)/2)
Suma y producto de raíces [src] 
suma
           ______________                      ______________                                ________________                        ________________
          /          ___      ___             /          ___      ___           ___         /            ___            ___         /            ___ 
  3      /  19   9*\/ 5     \/ 5      3      /  19   9*\/ 5     \/ 5      3   \/ 5         /    19   9*\/ 5       3   \/ 5         /    19   9*\/ 5  
- - +   /   -- + -------  - ----- + - - -   /   -- + -------  - ----- + - - + ----- - I*  /   - -- + -------  + - - + ----- + I*  /   - -- + ------- 
  2   \/    2       2         2       2   \/    2       2         2       2     2       \/      2       2         2     2       \/      2       2
(((−192+952−32−52)+(−32−52+192+952))+(−32+52−i−192+952))+(−32+52+i−192+952)\left(\left(\left(- \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}} - \frac{3}{2} - \frac{\sqrt{5}}{2}\right) + \left(- \frac{3}{2} - \frac{\sqrt{5}}{2} + \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right)\right) + \left(- \frac{3}{2} + \frac{\sqrt{5}}{2} - i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right)\right) + \left(- \frac{3}{2} + \frac{\sqrt{5}}{2} + i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right) 
=
-6
−6-6 
producto
/           ______________        \ /           ______________        \ /                     ________________\ /                     ________________\
|          /          ___      ___| |          /          ___      ___| |        ___         /            ___ | |        ___         /            ___ |
|  3      /  19   9*\/ 5     \/ 5 | |  3      /  19   9*\/ 5     \/ 5 | |  3   \/ 5         /    19   9*\/ 5  | |  3   \/ 5         /    19   9*\/ 5  |
|- - +   /   -- + -------  - -----|*|- - -   /   -- + -------  - -----|*|- - + ----- - I*  /   - -- + ------- |*|- - + ----- + I*  /   - -- + ------- |
\  2   \/    2       2         2  / \  2   \/    2       2         2  / \  2     2       \/      2       2    / \  2     2       \/      2       2    /
(−32−52+192+952)(−192+952−32−52)(−32+52−i−192+952)(−32+52+i−192+952)\left(- \frac{3}{2} - \frac{\sqrt{5}}{2} + \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right) \left(- \sqrt{\frac{19}{2} + \frac{9 \sqrt{5}}{2}} - \frac{3}{2} - \frac{\sqrt{5}}{2}\right) \left(- \frac{3}{2} + \frac{\sqrt{5}}{2} - i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right) \left(- \frac{3}{2} + \frac{\sqrt{5}}{2} + i \sqrt{- \frac{19}{2} + \frac{9 \sqrt{5}}{2}}\right) 
=
-9
−9-9 
-9
Respuesta numérica [src] 
x1 = -0.381966011250105 - 0.749870588001059*i
x2 = -7.04096354943126
x3 = -0.381966011250105 + 0.749870588001059*i
x4 = 1.80489557193147
x4 = 1.80489557193147
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