Question

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

Answer 1

Given,  (a−b)x²+(b−c)x+(c−a)=0  are equal.

Then the discriminant =0.

Then 

(b−c)²−4(c−a)(a−b)=0

(b²−2bc+c²)−4(ac−bc−a²+ab)=0

(b²+2bc+c²)−2a(b+c)+4a²=0

(b+c)²−2a(b+c)+4a²=0

(b+c−2a)2=0

2a=b+c.