Questions a1 a2 and a3

(b - c) x^{2} + (c - a) x + (a - b) = 0 Now, A = (b - c); B = (c - a); C = (a - b) Now, D = B^{2} - 4 AC = {(c - a)}^{2} - 4 (b - c) (a - b) = c^{2} + a^{2} - 2 ca - 4 ab + 4 b^{2} + 4 ac - 4 bc = {(a - 2 b + c)}^{2} Now, roots of the above equation are given by : x = \frac{- B + \sqrt{D}}{2 A} or x = \frac{- B - \sqrt{D}}{2 A} \Rightarrow x = \frac{- (c - a) + (a - 2 b + c)}{2 (b - c)} or x = \frac{- (c - a) - (a - 2 b + c)}{2 (b - c)} \Rightarrow x = \frac{(a - b)}{(b - c)} or x = 1

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