Here's the question you clicked on:
swissgirl
How to find the complex roots of \(x^4+x^3+3x^2+2x+2 \)
you have to factor out any real roots easiest to graph the function to obtain any real roots
There are no real roots though
let (x^2+bx+1)(x^2+cx+2) = that expression and find the value of b and c
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 :|
I imagine you could factor this by grouping and then use the quadratic formula again.
i tried doing the method u taught me yesterday but it wldnt go
\[\Large x^4+x^3+3x^2+2x+2 \\ \Large =x^4+2x^2+x^3+x^2+2(x+1)\\ \Large =x^4+2x^2+x^2(x+1)+2(x+1)\\ \Large =x^2(x^2+2)+(x^2+2)(x+1)\\ \Large =(x^2+2)(x^2+x+1)\]
I think the trick is seeing to split up the \(3x^2\) as \(2x^2+x^2\).
omg y is it always sooooo simple and I can never see it lol
Thanksssss guyssss for helping me :))))