Form polynomial equations of the lowest degree , with roots as given below
`2pm sqrt(3) ,1 pm 2i`

Explanation

Required equation is
`[x-(2+sqrt(3))] [x-(2-sqrt(3))]`
`[x-(1+2i)] [x-(1-2i)] =0 ………..(1)`
` [x-(2+sqrt(3))][x-(2-sqrt(3))] `
`=[(x-2)-sqrt(3) ] [(x-2)+sqrt(3)]`
=`(x-2)^2 -3`
`x^2 -4x +4 -3 `
` x^2-4x +1[x-(1+2i)][x-(1-2i)]`
[(x-1)-2i] [(x-1)+2i]
`(x-1)^2-4i^2`
=`(x^2-2x +1+4)`
`x^2 -2x+5 `
Substituting in (1) required equation is
`(x^2 -4x+1) (x^2 -2x+5) =0`
`rArr x^4 -4x^3+x^2-2x^3+8x^2-2x+5x^2-20x+5=0`
`rArr x^4-6x^3+14x^2 =22x +5 =0 `