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2014-08-15T13:15:24+05:30
Lets say that negative root is - \alpha

a \alpha ^{2} - b \alpha + c = 0 \\ c \alpha ^{2} - b \alpha + a = 0 \\ \\ \frac{ \alpha ^{2} }{-ba + bc} = \frac{ \alpha }{ c^{2} - a^{2} } = \frac{1}{-ba + bc} \\ \\ \frac{ \alpha ^{2} }{b(c - a)} = \frac{ \alpha }{(c - a) (c + a) } = \frac{1}{b(c - a)} \\ \\ \frac{ \alpha ^{2} }{b} = \frac{ \alpha }{c + a} = \frac{1}{b} \\ \\ \alpha = \frac{c + a}{b} \\ \alpha ^{2} = 1 \\ \\ \frac{(a + c)}{b} ^{2} = 1 \\ \\ (a + c)^{2} = b^{2} \\ (a + c)^{2} - b^{2} = 0
(a+c+b) (a+c-b) = 0

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