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

[knrao]

Hi
I need help to solve the polynomial equation
27X4+4KX-K=0 (K=0.9715)
Any one can help me
Thanks
Rao

 

[dextercioby]

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.

 

[tacman]

Hi Rao,

To solve this polynomial equation, we first need to substitute the given value of K into the equation. This will give us: 27X^4 + 4(0.9715)X - 0.9715 = 0.

Next, we can simplify the equation by combining like terms: 27X^4 + 3.886X - 0.9715 = 0.

Now, we can use various methods to solve for X, such as the rational root theorem or synthetic division. However, since this is a fourth-degree polynomial, it may be easier to use a graphing calculator or software to find the roots.

Using a graphing calculator, we can graph the equation and find the x-intercepts, which represent the solutions to the equation. In this case, the x-intercepts are approximately -0.488 and 0.237.

Therefore, the solutions to the equation are X = -0.488 and X = 0.237.

I hope this helps! Let me know if you have any further questions. Good luck with your problem-solving.