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Q.
Roots of the equation $(a+b-c) x^2-2 a x+(a-b+c)=0,(a, b, c \in Q)$ are-
Complex Numbers and Quadratic Equations
Solution:
$D=4 a^2-4[a-b+c](a+b-c) $
$ =4\left[a^2-\left\{a^2+a b-a c-a b-b^2+b c+a c+b c-c^2\right]\right. $
$=4\left[b^2+c^2-2 b c\right]=4(b-c)^2$
$D=\{2(b-c)\}^2$
Hence D is perfect square of a rational number
Hence (1)