## swissgirl 3 years ago How to find the complex roots of $$x^4+x^3+3x^2+2x+2$$

1. dumbcow

you have to factor out any real roots easiest to graph the function to obtain any real roots

2. swissgirl

There are no real roots though

3. swissgirl

its above the y axis

4. experimentX

let (x^2+bx+1)(x^2+cx+2) = that expression and find the value of b and c

5. dumbcow

ok then yeah what @experimentX said if two of the complex roots is in the form: $x = a \pm bi$ then $x-a = \pm bi$ $(x-a)^{2} = -b^{2}$ $x^{2}+ (-2a)x +(a^{2}+b^{2}) = 0$ anyway , my point is that a pair of complex roots come from a quadratic equation :|

6. KingGeorge

I imagine you could factor this by grouping and then use the quadratic formula again.

7. swissgirl

i tried doing the method u taught me yesterday but it wldnt go

8. KingGeorge

$\Large x^4+x^3+3x^2+2x+2 \\ \Large =x^4+2x^2+x^3+x^2+2(x+1)\\ \Large =x^4+2x^2+x^2(x+1)+2(x+1)\\ \Large =x^2(x^2+2)+(x^2+2)(x+1)\\ \Large =(x^2+2)(x^2+x+1)$

9. KingGeorge

I think the trick is seeing to split up the $$3x^2$$ as $$2x^2+x^2$$.

10. swissgirl

omg y is it always sooooo simple and I can never see it lol

11. swissgirl

Thanksssss guyssss for helping me :))))

12. KingGeorge

You're welcome.