If the roots of the equation (b-c)x^{2} +(c-a)x +(a-b) = 0 are equal show that a, b, c are in AP.
Ans: Refer sum No.12 of Q.E.
If (b-c)x^{2} + (c-a)x + (a-b)x have equal root.
B^{2}-4AC=0.
Proceed as in sum No.13 of Q.E to get c + a = 2b
⇒ b - a = c - b
⇒ a, b, c are in AP