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 the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then

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

If the sum of two roots of the equation x^3-px^2 + qx-r =0 is zero, then:

If the roots of the equation x^(3) - px^(2) + qx - r = 0 are in A.P., then prove that, 2p^3 −9pq+27r=0

If 2p^3 - 9pq + 27r = 0 then prove that the roots of the equations rx^3 - qx^2 + px - 1 = 0 are in H.P.

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 + px^2 + qx +r=0 may be in G.P is p^3 r=q^3

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

If sin alpha and cos alpha are roots of the equation px^2 + qx+r=0 then :

If a,b,c are the roots of the equation x^3+px^2+qx+r=0 such that c^2=-ab show that (2q-p^2)^3. r=(pq-4r)^3 .