If the zeroes of

We know, if p, q and r are the roots of a cubic equation then

For the given equation,

……[1]

……[2]

……[3]

As, roots are in AP we can let roots as (A – D), A, (A + D) [Where D is common difference]

From [1], we have

……[4]

From [2], we have

……[5]

From [3], we have

From [4] and [5]

⇒ 2b³ – 3abc + a²d = 0

Hence Proved!