Question

The roots of the equation (p – q) x² + (r – p) x +(q – r) = 0 are equal then 1/p, 1/q, 1/r are in-

• A. A.P.
• B. G.P.
• C. H.P.
• D. A.G.P.

Answer 1

Answer: (C)

H.P.

Answer 2

Here (p – q) x² + (r – p)x + (q – r) = 0

Put x = 1, (p – q) + (r – p) + (q – r) = 0

So both roots are x = 1, 1

Now sum of roots = 1 + 1 = $\frac{- (r - p)}{(p - q)}$

Ž 2 = $\frac{p - r}{p - q}$Ž 2p – 2q = p – r Ž 2q = p + r

Ž $\frac{1}{p}$,$\frac{1}{q}$,$\frac{1}{r}$are in H.P.