Question

if the roots of equation (a-b)x2+(b -c)x+(c-a)=0are equal,show that c,a and b are inAP

Answer 1

for equal roots discriminant must be zero...by
solving the equation [b^2-4ac=0]
at the end you will get the relation 2a=c+b ...and from this equation we conclude that b is Arithematic mean of a and c ...therefore c,a and b are in AP ..
I have given solution for a similar question to this in the photo ...