Let $T_n$ denotes the $n^{th }$ term of an arithmetic progression such that $T_p=\frac{1}{q}$ and $T_q=\frac{1}{p}$; Then which of the given option is necessarily a root to the equation $(p+2q-3r)x^2+(q+2r-3p)x+(r+2p-3q)=0$ given that $p+2q-3r\ne 0$