Finding x's of a 4th degree.

**EyesForEars** · February 11th 2009, 05:22 AM

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

$\sqrt{-2}$ ?

**ADARSH** · February 11th 2009, 05:35 AM

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?

**HallsofIvy** · February 11th 2009, 09:46 AM

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 $\sqrt{2}$ nor $i\sqrt{2}$ 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

**ADARSH** · February 14th 2009, 03:41 AM

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

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