Question

find the condition which must be satisfied of the polynomial

Answer 1

sum of three solutions of equation is -b/a
in this case it is -(-p)/1 i.e p
given sum of 2 solutions is 0 implies third solution must be p

so substituting p in the equation the equation must get the value as 0
so condition reqd is p^3-p^3+qp-r=0
implies qp=r is the reqd condition