Form polynomial equations of the lowest degree , with roots as given below
`1pm sqrt(3) ,2,5`

Explanation

Required equation is
`[x-(1+sqrt(3))] [x-(1-sqrt(3)) ] [(x-2) (x-5)]=0..... (1)`
`[x-(1+sqrt(3))] [x-(1-sqrt(3)) ]`
`=[(x-1)-sqrt(3)] [(x-1)+sqrt(3) ]`
`=(x-1)^2-3=x^2-2x+1-3`
`=x^2-2x-2`
` (x-2)(x-5)=x^2-2x-5x+10`
`=x^2=7x +10`
Substituting in (1) , required equation is
`(x^2=2x-2)(x^2-7x+10)=0`
`rArr x^4-2x^3-2x^2-7x^3+14x^2+14x+10x^2-20x-20=0`
`rArr x^4-9x^3+22x^2-6x-20=0`