Does my quartic have complex roots

[Uniquebum]

Homework Statement

Hey!

I don't really face a problem at the moment but i'd like someone to act as another brain for me. I've solved - hopefully right - a quartic equation and i get all the 4 roots out but 2 of them turn out to be complex numbers. Now, I'm fine with that but i'd also need to solve quartic inequality with the same polynomial. At the moment I'm not sure how i'd go about it with complex numbers so i'd love it if one of you checked the following and would confirm that the quartic really has complex roots.

[PLAIN]http://img842.imageshack.us/img842/5346/17817831.png

 

[vela]

Yes, those roots are correct. You can always use Wolfram Alpha to check your work.

 

[Uniquebum]

Alright, thanks a lot.

 

[ehild]

Your derivation is correct and the quadratic factor has really complex roots. But do not worry, you have to stay within the real numbers. The quadratic factor never changes sign, as it does not have real roots. It is positive for every real x.

ehild

 

[HallsofIvy]

What part of this problem says "you have to stay within the real numbers"?

 

[NascentOxygen]

You could just plot the graph, by hand or using software. The number of times any graph crosses the x-axis equals the number of real roots.

Note that complex roots always occur in pairs, too.

 

[HallsofIvy]

Complex roots of polynomial equations with real coefficients always occurs in conjugate pairs.