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

• knrao
In summary, a polynomial equation is an algebraic equation with terms containing non-zero coefficients and non-negative integer exponents. To solve it, you need to collect like terms, factor the equation, set the factors equal to zero and solve for the variable, and check your solutions. The degree of a polynomial equation is the highest exponent of the variable, and a coefficient that is a variable can be solved by isolating it and substituting the given value. When a specific value is given for a variable, you can substitute it in the equation and solve for the remaining variable using the same steps.
knrao
Hi
I need help to solve the polynomial equation
27X4+4KX-K=0 (K=0.9715)
Any one can help me
Thanks
Rao

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.

Last edited:

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.

## 1. What is a polynomial equation?

A polynomial equation is an algebraic equation that contains one or more terms with non-zero coefficients and non-negative integer exponents. It can be solved to find the values of the variable that make the equation true.

## 2. How do you solve a polynomial equation?

To solve a polynomial equation, you need to follow these steps:

1. Collect all like terms and group them together.
2. Factor the equation, if possible.
3. Set each factor equal to zero and solve for the variable.
4. Check your solutions by substituting them back into the original equation.

## 3. What is the degree of a polynomial equation?

The degree of a polynomial equation is the highest exponent of the variable in the equation. In the given equation, 27X4+4KX-K=0, the degree is 4.

## 4. How do you handle a coefficient that is a variable?

In the given equation, the coefficient 4K is a variable. To solve for the variable, you can isolate it on one side of the equation and then substitute the given value for K in the equation. For example, you could rewrite the equation as 27X4+4KX-K=0 as 4KX-K=-27X4 and then solve for K by dividing both sides by 4X, giving you K=-27X4/4X or K=-6.75.

## 5. How do you solve a polynomial equation when given a specific value for a variable?

In the given equation, the value of K is given as 0.9715. To solve for X, you can substitute this value for K in the equation and then solve for X. The equation would then become 27X4+4(0.9715)X-0.9715=0. From here, you can follow the steps mentioned earlier to solve for X.

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