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Question: If T<sub>n</sub> denotes the n<sup>th</sup> term of an A.P. and T<sub>p</sub>= \(\frac{1}{q}\), T<su...

If Tn denotes the nth term of an A.P. and Tp= 1q\frac{1}{q}, Tq = 1p\frac{1}{p}then which of the following is necessarily a root of the equation (p + 2q –3r) x2 + (q + 2r –3p) x +(r + 2p –3q) = 0 ?

A

Tp

B

Tq

C

Tpq

D

Tp+q

Answer

Tpq

Explanation

Solution

As p + 2q –3r + q +2r –3p + r +2p – 3q = 0

\ x = 1 is the root of the equation.