# Thread: Finding x's of a 4th degree.

1. ## Finding x's of a 4th degree.

I've tried factoring as best as I can, I've tried to apply what little I can understand about the rational roots theorem. I've tried grouping. All to no avail. I think it must be a tricky one.

Function is.
$\displaystyle f(x)=x^4+8x^3+6x^2-18x-10$
Thoughts? Any obvious giveaways I'm overlooking? Root at
$\displaystyle \sqrt{2}$

$\displaystyle \sqrt{-2}$?

2. If you want I can give you answer in decimals without solution( from calculator) but that will not be the ideal way to approach it, do you want it?

3. Factoring won't work because this equation has no rational roots. And it is easy to see, by putting them into the equation, that neither $\displaystyle \sqrt{2}$ nor $\displaystyle i\sqrt{2}$ is a solution.

You will have to resort to numerical solution, as ADARSH suggests, or the "quartic formula" which is very complicated: see
Solving Quartic Equations

4. I think that wont be a very difficult method after sufficient practice , any other methods?