show that the condition that the roots of ` x^3 + px^2 + qx +r=0` may be in
G.P is ` p^3 r=q^3`

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in h.P is 2q^3=r (3 pq -r)

show that the condition that the roots of x^3 + 3 px^2 + 3 qx +r=0 may be in A.P " is" 2p^3 -3pq +r=0

The condition that the roots of x^3 +3 px^2 +3qx +r = 0 may be in H.P. is

FIND that condition that the roots of equation ax^3+3bx^2+3cx+d=0 may be in G.P.

The condition that the product of two of the roots x^3 +px^2 +qx +r=0 is -1 is

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

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

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

If zeros of x^3 - 3p x^2 + qx - r are in A.P., then

Find the condition that the zeroes of the polynomial f(x) = x^3 – px^2 + qx - r may be in arithmetic progression.