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

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

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 -bx^2 +cx -d=0 are in G.P is

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

If the roots of the cubic equation ax^3+bx^2+cx+d=0 are in G.P then

Find the condition that the ratio between the roots of the equation ax^(2)+bx+c=0 may be m:n.

Find the condition in order that the equation ax^4+4bx^3+6cx^2+4dx+e=0 may have a pair of equal roots .

The condition that the root of ax^(2)+bx+c=0 may be in the ratio m: n is :

Find the condition that one root of the quadratic equation ax^(2)+bx+c=0 shall be n times the other, where n is positive integer.

Find the condition that one root of ax^(2)+bx+c=0 may be four times the other.