if the equation [b-c]x2+[c-a]x+a-c=0,,,,has equal roots then prove 2b=a+c

Dear aditya,

             I think there is some problem in question. As you have told equation has equal roots then its descriminant will be 0

so                        B²=4AC

                        [c-a]²=4[b-c][a-c]     on solving this you get 4b=3c+a