Question

if roots of the equation (a- b) x^2 +( b-c)x +( c-a) =0 are
equal, prove that 2a= b+c

Answer 1

Step-by-step explanation:

(a- b) x^2 +( b-c)x +( c-a) =0

D = B^2 - 4 AC

D = 0

B^2 - 4 AC = 0

[b-c]^2 - 4 [a-b][c-a] = 0

solving this, you get,

b^2 + c^2 + (2a)^2 -4ab - 4ac + 2bc = 0

[2a - b - c]^2 = 0                    {identity}

2a - b - c = 0

2a = b + c

∴hence proved

Answer 2

Here is ur answer hope this helps if so mark as brainliest.