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La ecuación:
Ecuación 3*x^2-x+2=0
Ecuación x^2=-74
Ecuación z^2+z+1=0
Ecuación 90+x-4*10=60
Expresar {x} en función de y en la ecuación:
9*x+14*y=-10
-4*x-8*y=-20
-12*x-10*y=-16
10*x-15*y=16
Expresiones idénticas
dos *x^ tres - siete *x^ dos + cinco *x- diecinueve = cero
2 multiplicar por x al cubo menos 7 multiplicar por x al cuadrado más 5 multiplicar por x menos 19 es igual a 0
dos multiplicar por x en el grado tres menos siete multiplicar por x en el grado dos más cinco multiplicar por x menos diecinueve es igual a cero
2*x3-7*x2+5*x-19=0
2*x³-7*x²+5*x-19=0
2*x en el grado 3-7*x en el grado 2+5*x-19=0
2x^3-7x^2+5x-19=0
2x3-7x2+5x-19=0
2*x^3-7*x^2+5*x-19=O
Expresiones semejantes
2*x^3+7*x^2+5*x-19=0
2*x^3-7*x^2+5*x+19=0
2*x^3-7*x^2-5*x-19=0

2x^3-7x^2+5*x-19=0 la ecuación

El profesor se sorprenderá mucho al ver tu solución correcta😉

Solución

Ha introducido [src]

   3      2               
2*x  - 7*x  + 5*x - 19 = 0

\left(5 x + \left(2 x^{3} - 7 x^{2}\right)\right) - 19 = 0

Simplificar

Teorema de Cardano-Vieta

reescribamos la ecuación

\left(5 x + \left(2 x^{3} - 7 x^{2}\right)\right) - 19 = 0

a x^{3} + b x^{2} + c x + d = 0

como ecuación cúbica reducida

x^{3} + \frac{b x^{2}}{a} + \frac{c x}{a} + \frac{d}{a} = 0

x^{3} - \frac{7 x^{2}}{2} + \frac{5 x}{2} - \frac{19}{2} = 0

p x^{2} + q x + v + x^{3} = 0

donde

p = \frac{b}{a}

p = - \frac{7}{2}

q = \frac{c}{a}

q = \frac{5}{2}

v = \frac{d}{a}

v = - \frac{19}{2}

Fórmulas de Cardano-Vieta

x_{1} + x_{2} + x_{3} = - p

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = q

x_{1} x_{2} x_{3} = v

x_{1} + x_{2} + x_{3} = \frac{7}{2}

x_{1} x_{2} + x_{1} x_{3} + x_{2} x_{3} = \frac{5}{2}

x_{1} x_{2} x_{3} = - \frac{19}{2}

Gráfica

Trazar el gráfico f1(x)

Trazar el gráfico f2(x)

Suma y producto de raíces [src]

suma

                                      __________________     /             __________________                             \                                         __________________     /           __________________                             \                                                           
                                     /         ________      |            /         ________                              |                                        /         ________      |          /         ________                              |                                                           
                                    /  527   \/ 122673       |    ___    /  527   \/ 122673                               |                                       /  527   \/ 122673       |  ___    /  527   \/ 122673                               |            __________________                             
                                 3 /   --- + ----------      |  \/ 3 *3 /   --- + ----------                  ___         |                                    3 /   --- + ----------      |\/ 3 *3 /   --- + ----------                  ___         |           /         ________                              
7               19               \/    108       72          |        \/    108       72                 19*\/ 3          |   7               19               \/    108       72          |      \/    108       72                 19*\/ 3          |   7      /  527   \/ 122673                 19            
- - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------| + - - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------| + - + 3 /   --- + ----------  + --------------------------
6           __________________              2                |                2                         __________________|   6           __________________              2                |              2                         __________________|   6   \/    108       72                __________________
           /         ________                                |                                         /         ________ |              /         ________                                |                                       /         ________ |                                        /         ________ 
          /  527   \/ 122673                                 |                                        /  527   \/ 122673  |             /  527   \/ 122673                                 |                                      /  527   \/ 122673  |                                       /  527   \/ 122673  
    72*3 /   --- + ----------                                |                                  72*3 /   --- + ---------- |       72*3 /   --- + ----------                                |                                72*3 /   --- + ---------- |                                 36*3 /   --- + ---------- 
       \/    108       72                                    \                                     \/    108       72     /          \/    108       72                                    \                                   \/    108       72     /                                    \/    108       72

\left(\frac{19}{36 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}\right) + \left(\left(- \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} + \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}\right)\right) + \left(- \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2}\right)\right)\right)

      /           __________________                             \     /             __________________                             \
      |          /         ________                              |     |            /         ________                              |
      |  ___    /  527   \/ 122673                               |     |    ___    /  527   \/ 122673                               |
      |\/ 3 *3 /   --- + ----------                  ___         |     |  \/ 3 *3 /   --- + ----------                  ___         |
7     |      \/    108       72                 19*\/ 3          |     |        \/    108       72                 19*\/ 3          |
- + I*|----------------------------- - --------------------------| + I*|- ----------------------------- + --------------------------|
2     |              2                         __________________|     |                2                         __________________|
      |                                       /         ________ |     |                                         /         ________ |
      |                                      /  527   \/ 122673  |     |                                        /  527   \/ 122673  |
      |                                72*3 /   --- + ---------- |     |                                  72*3 /   --- + ---------- |
      \                                   \/    108       72     /     \                                     \/    108       72     /

\frac{7}{2} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} + \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}\right) + i \left(- \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2}\right)

producto

/                                      __________________     /             __________________                             \\ /                                      __________________     /           __________________                             \\                                                           
|                                     /         ________      |            /         ________                              || |                                     /         ________      |          /         ________                              ||                                                           
|                                    /  527   \/ 122673       |    ___    /  527   \/ 122673                               || |                                    /  527   \/ 122673       |  ___    /  527   \/ 122673                               || /         __________________                             \
|                                 3 /   --- + ----------      |  \/ 3 *3 /   --- + ----------                  ___         || |                                 3 /   --- + ----------      |\/ 3 *3 /   --- + ----------                  ___         || |        /         ________                              |
|7               19               \/    108       72          |        \/    108       72                 19*\/ 3          || |7               19               \/    108       72          |      \/    108       72                 19*\/ 3          || |7      /  527   \/ 122673                 19            |
|- - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------||*|- - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------||*|- + 3 /   --- + ----------  + --------------------------|
|6           __________________              2                |                2                         __________________|| |6           __________________              2                |              2                         __________________|| |6   \/    108       72                __________________|
|           /         ________                                |                                         /         ________ || |           /         ________                                |                                       /         ________ || |                                     /         ________ |
|          /  527   \/ 122673                                 |                                        /  527   \/ 122673  || |          /  527   \/ 122673                                 |                                      /  527   \/ 122673  || |                                    /  527   \/ 122673  |
|    72*3 /   --- + ----------                                |                                  72*3 /   --- + ---------- || |    72*3 /   --- + ----------                                |                                72*3 /   --- + ---------- || |                              36*3 /   --- + ---------- |
\       \/    108       72                                    \                                     \/    108       72     // \       \/    108       72                                    \                                   \/    108       72     // \                                 \/    108       72     /

\left(- \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2}\right)\right) \left(- \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} + \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}\right)\right) \left(\frac{19}{36 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}\right)

19/2

\frac{19}{2}

19/2

Respuesta rápida [src]

                                           __________________     /             __________________                             \
                                          /         ________      |            /         ________                              |
                                         /  527   \/ 122673       |    ___    /  527   \/ 122673                               |
                                      3 /   --- + ----------      |  \/ 3 *3 /   --- + ----------                  ___         |
     7               19               \/    108       72          |        \/    108       72                 19*\/ 3          |
x1 = - - -------------------------- - ----------------------- + I*|- ----------------------------- + --------------------------|
     6           __________________              2                |                2                         __________________|
                /         ________                                |                                         /         ________ |
               /  527   \/ 122673                                 |                                        /  527   \/ 122673  |
         72*3 /   --- + ----------                                |                                  72*3 /   --- + ---------- |
            \/    108       72                                    \                                     \/    108       72     /

x_{1} = - \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} + \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}\right)

                                           __________________     /           __________________                             \
                                          /         ________      |          /         ________                              |
                                         /  527   \/ 122673       |  ___    /  527   \/ 122673                               |
                                      3 /   --- + ----------      |\/ 3 *3 /   --- + ----------                  ___         |
     7               19               \/    108       72          |      \/    108       72                 19*\/ 3          |
x2 = - - -------------------------- - ----------------------- + I*|----------------------------- - --------------------------|
     6           __________________              2                |              2                         __________________|
                /         ________                                |                                       /         ________ |
               /  527   \/ 122673                                 |                                      /  527   \/ 122673  |
         72*3 /   --- + ----------                                |                                72*3 /   --- + ---------- |
            \/    108       72                                    \                                   \/    108       72     /

x_{2} = - \frac{\sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2} - \frac{19}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + i \left(- \frac{19 \sqrt{3}}{72 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}}{2}\right)

              __________________                             
             /         ________                              
     7      /  527   \/ 122673                 19            
x3 = - + 3 /   --- + ----------  + --------------------------
     6   \/    108       72                __________________
                                          /         ________ 
                                         /  527   \/ 122673  
                                   36*3 /   --- + ---------- 
                                      \/    108       72

x_{3} = \frac{19}{36 \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}} + \frac{7}{6} + \sqrt[3]{\frac{\sqrt{122673}}{72} + \frac{527}{108}}

x3 = 19/(36*(sqrt(122673)/72 + 527/108)^(1/3)) + 7/6 + (sqrt(122673)/72 + 527/108)^(1/3)

Respuesta numérica [src]

x1 = -0.0248341974384107 - 1.63575352487962*i

x2 = 3.54966839487682

x3 = -0.0248341974384107 + 1.63575352487962*i

x3 = -0.0248341974384107 + 1.63575352487962*i

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Expresiones idénticas

Expresiones semejantes

2*x^3-7*x^2+5*x-19=0 la ecuación

Solución numérica:

Solución

2x^3-7x^2+5*x-19=0 la ecuación