Solve Polynomial Equation: 27X4+4KX-K=0 (K=0.9715) - Rao

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SUMMARY

The polynomial equation 27X4 + 4KX - K = 0, with K set to 0.9715, can be solved using quartic solving algorithms and computational tools. The solutions include complex and real roots: approximately 0.17958 ± 0.48229i, 0.23041, and -0.58959. These results demonstrate the application of numerical methods in solving higher-degree polynomial equations.

PREREQUISITES

  • Understanding of quartic equations and their properties
  • Familiarity with complex numbers and their representation
  • Knowledge of numerical methods for polynomial solving
  • Experience with computational tools for mathematical problem-solving

NEXT STEPS

  • Research algorithms for solving quartic equations, such as Ferrari's method
  • Explore numerical methods for polynomial root-finding, including Newton-Raphson
  • Learn about complex number operations and their applications in polynomial equations
  • Utilize software tools like MATLAB or Python libraries (e.g., NumPy) for polynomial computations

USEFUL FOR

Mathematicians, engineers, and students involved in advanced algebra, numerical analysis, or computational mathematics will benefit from this discussion.

knrao
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Hi
I need help to solve the polynomial equation
27X4+4KX-K=0 (K=0.9715)
Any one can help me
Thanks
Rao
 
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1.Use the alogorithm for solving a quartic.
2.Use a computer.

2.

[tex]27x^4+\allowbreak 3.\,886x-0.9715=0[/tex]

Solution is : [tex]\left\{ x\simeq .\,17958\,83748\,64723\,92446\,37443\,25198+.\,48229\,37667\,81214\,05384\,75340\,03169i\right\} ,[/tex]

[tex]\allowbreak \left\{ x\simeq .\,17958\,83748\,64723\,92446\,37443\,25198-.\,48229\,37667\,81214\,05384\,75340\,03169i\right\} ,\allowbreak[/tex]

[tex]\left\{ x\simeq .\,23041\,56601\,18966\,06539\,90038\,76249\right\} ,[/tex]

[tex]\allowbreak \left\{ x\simeq -.\,58959\,24098\,48413\,91432\,64925\,26645\right\}[/tex]

Daniel.
 
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