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If the roots of the equation (b-c)x2 +(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)x2 + (c-a)x + (a-b)x have equal root.
B2-4AC=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
(a+b)''2
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