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
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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.
 
Last edited:

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