Indeed Lengthy

Algebra Level 5

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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