If the roots of the equation (b – c)x2 + (c – a)x + (a – b) = 0 are equal, then prove that 2b = a + c.

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D Mukherjee

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Here the roots of the polynomial are 1 and (a-b)/(b-c) Given that they are equal. So a-b = b-c Therefore by transposition 2b = a+c
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