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(p+0,1)(3p^3+〖2p〗^2+p+0,1) la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
           /   3        2       1 \    
(p + 1/10)*|3*p  + (2*p)  + p + --| = 0
           \                    10/
(p+110)((p+(3p3+(2p)2))+110)=0\left(p + \frac{1}{10}\right) \left(\left(p + \left(3 p^{3} + \left(2 p\right)^{2}\right)\right) + \frac{1}{10}\right) = 0
Simplificar
Gráfica
-15.0-12.5-10.0-7.5-5.0-2.50.02.55.07.510.012.5-5000050000
Trazar el gráfico f1(x)
Trazar el gráfico f2(x)
Respuesta rápida [src] 
p1 = -1/10
p1=−110p_{1} = - \frac{1}{10} 
               2/3   3 ____
       4   7*10      \/ 10 
p2 = - - - ------- - ------
       9      90       9
p2=−49−7⋅102390−1039p_{2} = - \frac{4}{9} - \frac{7 \cdot 10^{\frac{2}{3}}}{90} - \frac{\sqrt[3]{10}}{9} 
           3 ____       2/3     /    ___ 3 ____       ___   2/3\
       4   \/ 10    7*10        |  \/ 3 *\/ 10    7*\/ 3 *10   |
p3 = - - + ------ + ------- + I*|- ------------ + -------------|
       9     18       180       \       18             180     /
p3=−49+10318+7⋅1023180+i(−103318+7⋅10233180)p_{3} = - \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{\sqrt[3]{10} \sqrt{3}}{18} + \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180}\right) 
           3 ____       2/3     /      ___   2/3     ___ 3 ____\
       4   \/ 10    7*10        |  7*\/ 3 *10      \/ 3 *\/ 10 |
p4 = - - + ------ + ------- + I*|- ------------- + ------------|
       9     18       180       \       180             18     /
p4=−49+10318+7⋅1023180+i(−7⋅10233180+103318)p_{4} = - \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180} + \frac{\sqrt[3]{10} \sqrt{3}}{18}\right) 
p4 = -4/9 + 10^(1/3)/18 + 7*10^(2/3)/180 + i*(-7*10^(2/3)*sqrt(3)/180 + 10^(1/3)*sqrt(3)/18)
Suma y producto de raíces [src] 
suma
                 2/3   3 ____         3 ____       2/3     /    ___ 3 ____       ___   2/3\         3 ____       2/3     /      ___   2/3     ___ 3 ____\
  1      4   7*10      \/ 10      4   \/ 10    7*10        |  \/ 3 *\/ 10    7*\/ 3 *10   |     4   \/ 10    7*10        |  7*\/ 3 *10      \/ 3 *\/ 10 |
- -- + - - - ------- - ------ + - - + ------ + ------- + I*|- ------------ + -------------| + - - + ------ + ------- + I*|- ------------- + ------------|
  10     9      90       9        9     18       180       \       18             180     /     9     18       180       \       180             18     /
(−49+10318+7⋅1023180+i(−7⋅10233180+103318))+(((−49−7⋅102390−1039)−110)+(−49+10318+7⋅1023180+i(−103318+7⋅10233180)))\left(- \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180} + \frac{\sqrt[3]{10} \sqrt{3}}{18}\right)\right) + \left(\left(\left(- \frac{4}{9} - \frac{7 \cdot 10^{\frac{2}{3}}}{90} - \frac{\sqrt[3]{10}}{9}\right) - \frac{1}{10}\right) + \left(- \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{\sqrt[3]{10} \sqrt{3}}{18} + \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180}\right)\right)\right) 
=
         /      ___   2/3     ___ 3 ____\     /    ___ 3 ____       ___   2/3\
  43     |  7*\/ 3 *10      \/ 3 *\/ 10 |     |  \/ 3 *\/ 10    7*\/ 3 *10   |
- -- + I*|- ------------- + ------------| + I*|- ------------ + -------------|
  30     \       180             18     /     \       18             180     /
−4330+i(−7⋅10233180+103318)+i(−103318+7⋅10233180)- \frac{43}{30} + i \left(- \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180} + \frac{\sqrt[3]{10} \sqrt{3}}{18}\right) + i \left(- \frac{\sqrt[3]{10} \sqrt{3}}{18} + \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180}\right) 
producto
 /          2/3   3 ____\                                                                                                                             
 |  4   7*10      \/ 10 |                                                                                                                             
-|- - - ------- - ------|  /      3 ____       2/3     /    ___ 3 ____       ___   2/3\\ /      3 ____       2/3     /      ___   2/3     ___ 3 ____\\
 \  9      90       9   /  |  4   \/ 10    7*10        |  \/ 3 *\/ 10    7*\/ 3 *10   || |  4   \/ 10    7*10        |  7*\/ 3 *10      \/ 3 *\/ 10 ||
--------------------------*|- - + ------ + ------- + I*|- ------------ + -------------||*|- - + ------ + ------- + I*|- ------------- + ------------||
            10             \  9     18       180       \       18             180     // \  9     18       180       \       180             18     //
−−49−7⋅102390−103910(−49+10318+7⋅1023180+i(−103318+7⋅10233180))(−49+10318+7⋅1023180+i(−7⋅10233180+103318))- \frac{- \frac{4}{9} - \frac{7 \cdot 10^{\frac{2}{3}}}{90} - \frac{\sqrt[3]{10}}{9}}{10} \left(- \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{\sqrt[3]{10} \sqrt{3}}{18} + \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180}\right)\right) \left(- \frac{4}{9} + \frac{\sqrt[3]{10}}{18} + \frac{7 \cdot 10^{\frac{2}{3}}}{180} + i \left(- \frac{7 \cdot 10^{\frac{2}{3}} \sqrt{3}}{180} + \frac{\sqrt[3]{10} \sqrt{3}}{18}\right)\right) 
=
1/300
1300\frac{1}{300} 
1/300
Respuesta numérica [src] 
p1 = -0.144247395913287 - 0.105335390924392*i
p2 = -0.144247395913287 + 0.105335390924392*i
p3 = -0.1
p4 = -1.04483854150676
p4 = -1.04483854150676
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