Form polynomial equations of the lowest degree , with roots as given below
0,1,-`3/2,-5/2`

Explanation

Required equation is
`x(x-1)(x+3/2)(x+5/2)=0 ........(1) `
`x(x-1)=x^2-x`
`(x+3/2)(x+5/2)=x^2+3/2x+5/2x+(15)/(4)=x^2+4x+(15)/(4)`
Substituting in (1) ,required equation is
`rArr (x^2-x)(x^2+4x+(15)/(4))=0`
`rArr x^4-x^3+4x^3-4x^2+(15)/(4)x^2-(15x)/(4)=0`
`x^4+3x^3-1/4x^2-(15)/(4)x=0`
`or rArr 4x^4+12x^3-x^2-15x=0`