Question

If the roots of the quadratic equation (a - b)

2 + (b - c) + (c - a) = 0 are equal, prove that

2a = b +c​

Answer 1

Answer:

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

or, (b²−2bc+c²) − 4(ac−bc−a²+ab) = 0

or, (b²+2bc+c²) − 2a(b+c)+4a² = 0

or, (b+c)² − 2a(b+c) + 4a² = 0

or, (b+c−2a)² = 0

or, 2a = b + c