# Finding the domain of the square root of a polynomial

1. Jan 4, 2008

I was just going through some problems in a maths journal for undergraduate level

i found a sum seeming simple but i am not able to solve it completly

find domain of $$\sqrt{x^{12} - x^9 + x^4 -x +1}$$

i know domain includes all negative value , all positive value >1 , but i cant get anything about (0,1)

Last edited: Jan 4, 2008
2. Jan 5, 2008

### Rainbow Child

For $$x\in [0,1]\Rightarrow x-1\leq0$$

Now don't bother with the term x12, it is always positive, and factor the rest terms, i.e.

$$x^{12}-x^9+x^4-x+1=x^{12}-x^4(x^5-1)-(x-1)=x^{12}+x^4(1-x^5)+(1-x)\geq0$$

as sum of non negative numbers.

3. Jan 6, 2008