using synthetic division, I do not come up with any zeros for this polynomial f(x)= -x^4 - x + 5, but there has to be. what are my next steps?

Question

using synthetic division, I do not come up with any zeros for this polynomial f(x)= -x^4 - x + 5, but there has to be.  what are my next steps?

anonymous · Answer

Yeah, the roots are nasty on this one.  There are two roots.  Use a graphing calculator or WolframAlpha to find them.

anonymous · Answer

*You can't use synthetic division to find these two roots, by the way, because synthetic division can only be used to find rational roots.  These two are irrational.

anonymous · Answer

Even wolfram alpha doesn't give the exact answer, so my guess is that it's not mathematically possible to get an exact answer, only approximations.

anonymous · Answer

It does give an exact answer.  Under the "real roots" section, you can click on the "exact forms" button to give you get radicals

anonymous · Answer

hmmm, i'm poking around wolfram now.  it's my first time using it

anonymous · Answer

It's fun.  Just copy and paste your function in there:
-x^4-x+5

It'll give you lots of information about the function.  Also see attached.

anonymous · Answer

You're my hero, this is awesome, thank you!

anonymous · Answer

Sure thing :)