Find the sum of the squares and the sum of the cubes of the roots of the equations `x^3-px^2+qx-r=0` in terms of p,q,r

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

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) -2px^(2)+3qx -4r=0 is zero, then the value of r 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 G.P p^3 r= q^3

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

If the roots of the equation q^(2)x^(2)+p^(2)x+r^(2)=0 are the squares of the roots of the equation qx^(2)+px+r=0 , are the squares of the roots of the equation qx^(2)+px+r=0 , then q, p, r are in:

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

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