If \(\color{red}{T_n} \) denotes the \(\color{red}{n^{th}}\) term of an arithmetic progression such that \(\color{green}{T_p\,=\,\frac{1}{q}}\) and \(\color{green}{T_q\,=\,\frac{1}{p}}\), then which of the given option is necessarily a root to the equation \[\color{green}{(p+2q-3r)x^{2}\,+\,(q+2r-3p)x\,+\,(r+2p-3q)\,=\,0}\]

,given that \(\color{green}{p+2q-3r \neq 0}\).

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