if polynomial `p(x) = Ax^3 + Bx^2 + Cx + D` vanishes at `x = a-d, a, a + d`, then prove that `a^2+D/(aA)>0`. Here `A, B, C, D` are some constant.

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c , then a, b, c, d are in

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 a,b,c,d are in GP then prove that ax^3+bx^2+cx+d has a factor ax^2+c .

Consider a cubic polynomial p(x)=ax^(3)+bx^(2)+cx+d where a,b,c,d are integers such that ad is odd and bc is even. Prove that not all roots of p(x) can be rational

If ax^3 + bx^2 + cx + d is divisible by ax^2 + c, then a, b, c, d are in (a) AP (b) GP (c) HP

Two zeros of polynomial ax^3+bx^2+cx+d are zero then its third zero is a/b b/a -b/a d/c

IF x^2+ ax +b, x^2 + cx +d has the common factor x-1 then a+b -c-d=

Evaluate Lt_(xtooo)((x^(2)+ax+b)/(x^(2)+cx+d))^(x) where a, b, c, d are constants.