Question

if the roots of the equation (a - b)x' +(b-c)x+ (c-a)=0 are equal ,show that c,a and b are in AP.​

Answer 1

Answer:

(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

Answer 2

Step-by-step explanation:

Hope it will help you....