Question

Find all possible complex roots of x^4-3x^3-6x^2+8x and of x^3+10x^2+169x

Answer 1

Hello,

1)

`x^(4)-3x^(3)-6x^(2)+8x=x(x^3-3x^2-6x+8)`


`=x(x^(3)-x^(2)-2x^2+2x-8x+8)=x(x^(2)(x-1)-2x(x-1)-8(x-1))`


`=x(x-1)(x^2-2x-8)=x(x-1)(x^2+2x-4x-8)`


`=x(x-1)(x(x+2)-4(x+2))=x(x-1)(x+2)(x-4)`


2)


`x^(3)+10x^(2)+169x=x(x^2+10x+169)=x(x+5-12i)(x+5+12i)`