If a, b and c are three distinct real numbers and _ x (b-c) x^2+(c-a) x+(a-b) (a-b) x^2+(b-c) x+(c-a) = 1 2 , then a+2 c=

Step-by-step solution

_ x (b-c) x^2+(c-a) x+(a-b) (a-b) x^2+(b-c) x+(c-a) = 1 a = _ x x^2 x^2 [ (b-c)+(c-a) 1 x + (a-b) x^2 (a-b)+(b-c) 1 x + (c-a) x^2 ]= 1 2 = b-c a-b = 1 2 aligned & 2 b-2 c=a-b & 3 b=a+2 c aligned