Question

If the roots of the equation (a-b)x² + (b-c) x+ (c - a)= 0 are equal. Prove that 2a=b+c.

Answer 1

(a-b)x² + (b-c) x+ (c - a) = 0
T.P 2a = b + c
B² – 4AC = 0
(b-c)² – [4(a-b) (c - a)] = 0
b²-2bc + c² – [4(ac-a² – bc + ab)] = 0

=> b²-2bc + c² – 4ac + 4a² + 4bc - 4ab = 0
=> b²+ 2bc + c² + 4a² – 4ac – 4ab= 0
=> (b + c - 2a)² = 0
=> b + c = 2a