2010/024) If the roots of [b-c]x*x+[c-a]x+[a-b]=0are equal then prove that 2b=a+c

roots are equal so discriminant is zero

so (c-a)^2 - 4(b-c)(a-b) = 0

or c^2-2 ac + a^2 - 4(ab-ac- b^2 + bc) = 0

or a^2+4b^2+c^2+2ac - 4ab - 4bc = 0

or(a+c-2b)^2 = 0

or a+c-2b = 0 or a + c = 2b

proved