How to find the complex roots of
$x^4+x^3+3x^2+2x+2 $

Question

How to find the complex roots of 
$x^4+x^3+3x^2+2x+2 $

dumbcow · Answer

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

swissgirl · Answer

There are no real roots though

swissgirl · Answer

its above the y axis

experimentx · Answer

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

dumbcow · Answer

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 :|

kinggeorge · Answer

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

swissgirl · Answer

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

kinggeorge · Answer

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

kinggeorge · Answer

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

swissgirl · Answer

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

swissgirl · Answer

Thanksssss guyssss for helping me :))))

kinggeorge · Answer

You're welcome.