Show that a, b, c are in arithmetic progressions, Mathematics

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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

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