## swissgirl Group Title How to find the complex roots of $$x^4+x^3+3x^2+2x+2$$ one year ago one year ago

1. dumbcow Group Title

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

2. swissgirl Group Title

There are no real roots though

3. swissgirl Group Title

its above the y axis

4. experimentX Group Title

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

5. dumbcow Group Title

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 Group Title

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

7. swissgirl Group Title

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

8. KingGeorge Group Title

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

9. KingGeorge Group Title

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

10. swissgirl Group Title

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

11. swissgirl Group Title

Thanksssss guyssss for helping me :))))

12. KingGeorge Group Title

You're welcome.