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 the equation ax^3+bx^2+cx+d=0 may be in A.P., if (i)2b^3+27a^2d=9abc (ii)2b^3+27a^2d=-9abc (iii) 2b^3-27a^2d=9abc (iv) 2b^3-27a^2d=-9abc

The condition that the roots of the equation ax^3+bx^2+cx+d=0 may be in A.P., if (i) 2b^3+27a^2d=9abc (ii) 2b^3+27a^2d=-9abc (iii) 2b^3-27a^2d=9abc (iv) 2b^3-27a^2d=-9abc

The condition that the roots of ax^(3)+bx^(2)+cx+d =0 may be in G.P is

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

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

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

If the roots of the equation x^(3) + bx^(2) + cx - 1 = 0 form an increasing G.P., then b belongs to the interval

[Using Rolle's theorem show that between any two distinct real roots of equation ax^(3)+bx^(2)+cx+d=0, there is at least one root of equation 3ax^(2)+2bx+c=0.]

The condition that one root of ax^(3)+bx^(2)+cx+d=0 may be the sum of the other two is 4abc=