(a) Given equation is $x^{2} - 1005x + 2006 = 0$ $\Rightarrow \ (x - 2)(x - 1003) = 0$ $\Rightarrow \ x = 2,\ \ x = 1003$ $\therefore$ Required distance between the lines $= 1003 - 2 = 1001$
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Ph.D. in Physics with 19+ years of teaching experience.