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

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on comparing given equation with Ax²+Bx+C=o

A=(b-c), B=(c-a), C=(a-b)

now sum of roots=-B/A

α+α=-(c-a)/(b-c)

2α=a-c/(b-c)......1

product of roots=C/A

α²=(a-b)/(b-c)

putting the value of α from 1

on solving we get 2b=a+c