Question

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

Answer 1

Given, (a−b)x

2

+(b−c)x+(c−a)=0 are equal.

Then the discriminant =0.

Then

(b−c)

2

−4(c−a)(a−b)=0

or, (b

2

−2bc+c

2

)−4(ac−bc−a

2

+ab)=0

or, (b

2

+2bc+c

2

)−2a(b+c)+4a

2

=0

or, (b+c)

2

−2a(b+c)+4a

2

=0

or, (b+c−2a)

2

=0

or, 2a=b+c.