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If the zeros of the polynomial f(x)=ax^3...

If the zeros of the polynomial `f(x)=ax^3+3bx^2+3cx+d` are in A.P. then show that `2b^3-3abc+a^2d=0`

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According to question
`alpha-d+alpha+alpha+d=(-3b)/a`
`3alpha=(-3b)/a`
`alpha=-b/a`
`alpha^2-dd+alpha^2+alphad+alpha^2-d^2=(3)/a`

`3alpha^2-d^2=(3c)/a`
`3b^2/a^2-h^2=(3c)/a`
`d^2=(3b^2)/a^2-(3c)/a=(3b^2-3ac)/a^2`
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