If the ratio of the polynomial ax cube+3bx square+3cx+d are in A.P.Prove that 2b cube -3abc + a square d=0

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If roots of polynomial ax^3+3bx^2+3cx+d are in A.p. prove that 2b^3-3abc+a^2d=0

f (x) = a x^{3} + 3 b x^{2} + 3 c x + d

2 b^{3} - 3 a b c + a^{2} d = 0

p (x) = a x^{3} + 3 b x^{2} + 3 c x + d

2 b^{3} - 3 a b c + a^{2} d

a x^{3} + 3 b x^{2} + 3 c x + d = 0

If zeros of f(x)= ax³+3bx²+3cx+d are in arrithmatic progression , prover that 2b³-3abc+a²d=0

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