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

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 .

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

If alpha, beta, gamma are the zeros of the polynomial f(x) = ax^(3) + bx^(2) + cx + d then (alpha)^2 + (beta)^2 + (gamma)^2 = ………….

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