If $x - 1$ completely divides the equation $2 x^{2} + 3 x + (k - 9) = 0$ , then the value of $k$ is

5

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2

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3

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4

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Solution

The correct option is D $4$
If $(x - 1)$ divides given equation, then $1$ is a root of the equation.
If we substitute the root of equation, the value of equation should be zero.
Given equation, $2 x^{2} + 3 x + (k - 9) = 0$ substitute $x = 1$ in it
$\Rightarrow 2 (1)^{2} + 3 (1) + (k - 9) = 0$
$\Rightarrow 5 + k - 9 = 0$
$\Rightarrow k = 4$

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