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(D) Let $f(x) = x^{2}-3x+k$. For the roots to lie in the interval $(0,1)$,the vertex of the parabola must lie within $(0,1)$. The $x$-coordinate of th

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no value of $k$ satisfies the requirement

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(D) Let $f(x) = x^{2}-3x+k$. For the roots to lie in the interval $(0,1)$,the vertex of the parabola must lie within $(0,1)$. The $x$-coordinate of the vertex is given by $x = -\frac{b}{2a} = -\frac{-3}{2(1)} = \frac{3}{2} = 1.5$. Since $1.5 
otin (0,1)$,it is impossible for both roots to lie in the interval $(0,1)$ simultaneously. Therefore,there is no value of $k$ that satisfies the given condition.

The number of values of $k,$ for which the equation $x^{2}-3x+k=0$ has two distinct roots lying in the interval $(0,1),$ is

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