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

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To solve the polynomial equation 27X^4 + 4KX - K = 0 with K = 0.9715, the recommended approaches include using a quartic solving algorithm or computational tools. The solutions to the equation include two complex roots approximately equal to 0.17958 ± 0.48229i, one real root around 0.23042, and another real root approximately -0.58959. These results provide a comprehensive overview of the roots for the specified polynomial equation. The discussion emphasizes the utility of both analytical and numerical methods for solving quartic equations.
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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.

27x^4+\allowbreak 3.\,886x-0.9715=0

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

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

\left\{ x\simeq .\,23041\,56601\,18966\,06539\,90038\,76249\right\} ,

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

Daniel.
 
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