UPSC CDS Math Quadratic Equations and Inequations Questions

a(b−c)+b(c−a)+c(a−b)=0
Therefore, x = 1 is the root of the given equation.
It is given that roots of the equation are equal. So, both the roots of the equation are 1.
Therefore, product of the roots = 1
⇒

c(a−b)

a(bb−c)

=1
⇒ca−bc=ab−ac
⇒2ca=bc+ab
⇒

2

b

=

1

a

+

1

c