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Q.

The number of integral values of $k$ , for which one root of the equation $2 x^{2} - 8 x + k = 0$ lies in the interval (1, 2) and its other root lies in the interval (2, 3), is:

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a

2

b

1

c

0

d

3

answer is D.

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Detailed Solution

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$\begin{array}{l} f (x) = 2 x^{2} - 8 x + k = 0 \\ f (1) > 0; f (3) > 0 and f (2) < 0 \end{array}$
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$\begin{array}{l} \Rightarrow f (1) = - 6 + k > 0 \Rightarrow k > 6 \\ f (2) < 0 k - 8 + k < 0 \Rightarrow k < 8 \\ f (3) > 0 \Rightarrow - 6 + k > 0 \Rightarrow k > 6 \\ ∴ k \in (6, 8) \end{array}$

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