Question

If the roots of the equation (b – c) x² + (c – a) x + (a – b) = 0

be equal then a, b, c are in

• A. A.P.
• B. G.P.
• C. H.P.
• D. None of these

Answer 1

Answer: (A)

A.P.

Answer 2

Given equation (b – c) x² + (c – a) x + (a – b) = 0

Putting x = 1, we get

(b – c) + (c – a ) + (a – b) = 0

So x = 1 is a root but both roots are equal so both roots are 1, 1

Now sum of roots 1 + 1 = $\frac{- (c - a)}{(b - c)}$

Ž 2 = $\frac{- (c - a)}{(b - c)}$ Ž 2b – 2c = – c + a

Ž 2b = a + c

Ž a, b, c A.P.