If $(2 x + 5)$ is a factor of $2 x^{2} - k$ , then the value of $k$ is.

25/2

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Solution

The correct option is B. $\frac{25}{2}$
Let $p (x) = 2 x^{2} - k$ . If $(2 x + 5)$ is a factor of $2 x^{2} - k$ , then, $p (\frac{- 5}{2}) = 0$
$\Rightarrow p (\frac{- 5}{2}) = 2 (\frac{- 5}{2})^{2} - k = 0$
$\Rightarrow 2 \times \frac{25}{4} - k = 0$
$\Rightarrow k = \frac{25}{2}$

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