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Question: If a(b – c)x<sup>2</sup> + b(c – a) x + c(a – b) has equal roots, then a, b, c are in...

If a(b – c)x2 + b(c – a) x + c(a – b) has equal roots, then a, b, c are in

A

G.P.

B

A.P.

C

H.P.

D

Increasing order

Answer

H.P.

Explanation

Solution

The equation will have equal roots if

b2 (c – a)2 = 4ac (b – c) (a – b)

If we make a quadratic equation in b, we get

Ž a, b, c are in H.P. b = 2aca+c\frac{2ac}{a + c}