If the equation frac{1}{x} + frac{1}{x - 1} + | vedclass

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(C) Let $f(x) = \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}$ and $g(x) = 3x^3$.To find the number of real roots,we analyze the intersection of the

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$4$

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(C) Let $f(x) = \frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2}$ and $g(x) = 3x^3$.To find the number of real roots,we analyze the intersection of the graphs of $f(x)$ and $g(x)$.The function $f(x)$ has vertical asymptotes at $x = 0$,$x = 1$,and $x = 2$.By plotting the graph of $f(x)$ and the cubic function $g(x) = 3x^3$,we observe the points of intersection.As shown in the graph,the curves intersect at $4$ distinct points.Therefore,the equation has $4$ real roots,so $k = 4$.

If the equation $\frac{1}{x} + \frac{1}{x - 1} + \frac{1}{x - 2} = 3x^3$ has $k$ real roots,then $k$ is equal to -

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