If the equation `x^3+px^2+qx+1=0(p < q)` has only one real root `alpha` then `alpha` belongs to

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in A.P 2p^3 - 9 pq + 27 r=0

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in A.P 2p^3 - 9 pq + 27 r=0

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P 2p^3 =9r (pq-3r)

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in G.P p^3 r= q^3

Show that the roots of the equation x^3 +px^2 +qx +r=0 are in H.P then 2q^3 =9r (pq-3r)

If alpha is the only real root of the equation x^(3)+px^(2)-qx+1=0 and p+q<0. Then |[tan^(-1)a+tan^(-1)(a^(-1))]|... where [..1 is the greatest integer function.

What is the condition that the roots of the equation x^3+ px^2 + qx + r = 0 are in G.P.

If the roots of the equation, x^3 + px^2+qx-1 = 0 form an increasing G.P. where p and q are real,then

If the roots of the equation x^3 +3px^2 + 3qx -8=0 are in a geometric progression , then (q^3)/( p^3) =

If the roots of the equation x^3 +3px^2 + 3qx -8=0 are in a geometric progression , then (q^3)/( p^3) =