Question

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

Answer 1

Answer:

Step-by-step explanation:

As roots are  equal ,

b² - 4 a  c = 0

(b -c)² - 4 x a-b x c-a = 0

b² + c² - 2bc - 4 ( ac - a² - bc + ab ) = 0

b² + c² - 2bc - 4 ac + 4 a² + 4 bc - 4 ab = 0

b² + c²+ 4 a²- 4 ac - 4 ab + 2 bc = 0

(b+c-2a)²= 0 ( Identity:- a²+b²+c²+2ab+2bc+2ac)

b+c =  2 a ( Sq goes right side )

Answer 2

plz refer to this attachment