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`.

If a, b and c are roots of the equation x^3+qx^2+rx +s=0 then the value of r is

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

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

If alpha , beta , gamma are the roots of the equation x^3 +px^2 +qx +r=0 then sum alpha^2 ( beta + gamma)=

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

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 alpha , beta , gamma are the roots of the equation x^3 +px^2 + qx +r=0 prove that ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =r-pq

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 sum of the two roots of x^3 +px^2 +qx +r=0 is zero then pq=