Given that roots of `x^3+3px^2+3qx+r=0` are in
(i)A.P., show that `2p^3-3qp+r=0`

Explanation

Given equation is `x^3+3px^2+3qx+r=0`
(i) The roots are in A.P
Suppose a -d,a a+d are the roots
sum =a-d+a+a+d=-3p
3a=-3p`rArr` a=-p ……….(1)
`because` 'a' is a root of `x^3+3px^2+3qx+r=0 `
`rArr a^3 +3pa^2+3qa(-p)+r=0`
`rArr 2p^3-3pq +r=0 ` is the required condition