Largest interval in which x^12-x^9+x^4-x+1 is positive is

Question

loser66 · Answer

Use @rational root test :) we can see that possible roots are $\pm 1$, but neither of them gives us the root, hence it has no root.
Use graph, we see that the expression is positive for all x
Hence the largest interval is $(-\infty, \infty)$

anonymous · Answer

@Loser66  that is an unsubstantiated claim; that rules out rational roots but not irrational ones

loser66 · Answer

https://www.desmos.com/calculator/kdesqhqjgz

anonymous · Answer

very sry was away

anonymous · Answer

Calculators are actually not allowed

loser66 · Answer

@oldrin.bataku  is you the "high-school" student who made me feel as if I am an elementary baby in math?? hehehe... If you are that guy, I rather run away than stay and make any argument.

anonymous · Answer

yes, by graphing to the point that $x^{12}>x^9-x^4+x-1$ we can demonstrate there are no irrational roots, either, but this is not rigorous proof :p

anonymous · Answer

is there any other way