JEE MAIN - Mathematics (2023 - 1st February Evening Shift - No. 9)
The number of integral values of k, for which one root of the equation $$2x^2-8x+k=0$$ lies in the interval (1, 2) and its other root lies in the interval (2, 3), is :
2
0
1
3
Explanation
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$$ \begin{aligned} & f(1)>0 \Rightarrow k>6 \\\\ & f(2)<0 \Rightarrow k<8 \\\\ & f(3)>0 \Rightarrow k>6 \\\\ & k \in(6,8) \end{aligned} $$
Only 1 integral value of $k$ is 7.
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