# Homework Help: Does my quartic have complex roots

1. Sep 18, 2011

### Uniquebum

1. The problem statement, all variables and given/known data
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 [Broken]

Last edited by a moderator: May 5, 2017
2. Sep 18, 2011

### vela

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

3. Sep 18, 2011

### Uniquebum

Alright, thanks alot.

4. Sep 18, 2011

### 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

5. Sep 18, 2011

### HallsofIvy

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

6. Sep 22, 2011

### Staff: Mentor

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.

7. Sep 22, 2011

### HallsofIvy

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