Writing a Finite Polynomial for (k)1/2 in Math | Real Numbers

[mesa]

I need to write, (k)^1/2= a finite term polynomial of 'k' where 'k' is the set of all Reals where 'k' is greater than 0 in math.

Thanks!

 

[disregardthat]

You can't write $\sqrt{k}$ as a polynomial in k over $\mathbb{R}$.

 

[mesa]

You can't write $\sqrt{k}$ as a polynomial in k over $\mathbb{R}$.

That is interesting because you can, but that isn't the question. How do I go from my statement to 'math'.

 

[micromass]

You can't write $\sqrt{k}$ as a polynomial in k over $\mathbb{R}$.

This.

Thread locked.

 

[CellCoree]

I understand the importance of accurately representing mathematical concepts and equations. In this case, (k)1/2 represents the square root of k, where k is a real number greater than 0.

To write a finite term polynomial for (k)1/2, we can express it as k^(1/2), which can be expanded using the binomial theorem as (1/2)k^(1/2) + (1/2)k^(0.5-1) + (1/8)k^(0.5-2) + … + (1/n)k^(0.5-n), where n is the desired degree of the polynomial.

In simpler terms, the finite term polynomial for (k)1/2 would be a sum of terms with coefficients that decrease by 1/n and powers of k that decrease by 0.5 for each subsequent term.

For example, if we want a polynomial of degree 3, the finite term polynomial for (k)1/2 would be (1/2)k^(1/2) + (1/2)k^0 + (1/8)k^(-0.5) + (1/24)k^(-1). This can be simplified further as (1/2)√k + (1/2) + (1/8)/√k + (1/24)/k.

I hope this helps to accurately represent (k)1/2 as a finite term polynomial in the set of all real numbers where k is greater than 0.