Question
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 = a+c2ac