- #1

roni1

- 20

- 0

Why we can't use radical to solve an equations with power greater than 4?

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In summary, it is possible to solve certain equations with powers higher than 4, such as those in the form of $x^n-a=0$, $x^{2n}+x^n+a=0$, etc. However, the general fifth degree or higher polynomial cannot be solved using radicals due to the Abel-Ruffini Theorem. This theorem states that there are no solutions in radicals for general polynomial equations of degree five or higher with arbitrary coefficients.

- #1

roni1

- 20

- 0

Why we can't use radical to solve an equations with power greater than 4?

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- #2

cbarker1

Gold Member

MHB

- 349

- 23

- $x^n-a=0$
- $x^{2n}+x^n+a=0$
- $x^{3n}+x^{2n}+x^n+a=0$
- $x^{4n}+x^{3n}+x^{2n}+x^n+a=0$
- etc.

However, the general fifth degree or higher polynomial does not have a radical solution due to a theorem, Abel-Ruffin Theorem. there is no solutions in radical to general polynomial equations of degree five or higher with arbitrary coefficients.

Note: it does not assert some higher-degree polynomials have no solutions... (see at the beginning of the post)

A solution to a function with power greater than 4 is a value or set of values that satisfy the equation when substituted into the function.

To solve a function with power greater than 4, you can use various methods such as factoring, graphing, or using the quadratic formula depending on the specific function and its form.

Yes, a function with power greater than 4 can have multiple solutions, especially if it is a polynomial function. These solutions may be real or complex numbers.

To check if a value is a solution to a function with power greater than 4, simply substitute the value into the function and see if it satisfies the equation. If the output is equal to the input, then the value is a solution.

Yes, a function with power greater than 4 can have no solutions. This can occur if the function is undefined for all values or if the solutions are complex numbers and the function only deals with real numbers.

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