If the zeros of the polynomial `f(x)=a x^3+3b x^2+3c x+d` are in A.P., prove that `2b^3-3a b c+a^2d=0` .

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

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^(2)d=0

If zeros of a polynomial f(x) = ax^(3) + 3bx^(2) + 3cx + d are in AP prove that 2b^(3) - 3abc + a^(2) d = c .

If zeros of the polynomial f(x)=x^3-3p x^2+q x-r are in A.P., then (a) 2p^3=p q-r (b) 2p^3=p q+r (c) p^3=p q-r (d) None of these

In the polynomial p(x)= a x^ 3 + b x^ 2 + c x + d if p(2)=p(-2), prove that 4a+c=0.

If the zeros of the polynomial f(x)=x^(3)-3x^(2)+x+1 are a-b,quad a,a+b, find a and b

find the zeroes of the polynomial f(x) = x^3-12x^2 +39x -28 , if the zeroes are in A.P

If zeros of polynomial f(x0 = x^(3) - 3px^(2)+qx-r are in AP then 2p^(3) = ………..

If the zeros of the polynomial f(x)=x^3-3x^2+x+1 are a-b ,\ \ a ,\ \ a+b , find a and b .

Find the condition that the zeros of the polynomial f(x)=x^3+3p x^2+3q x+r may be in A.P.