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Remainder Theorem

If x - 4 is...

Question

If $x - 4$ is one of the factor of $x^{2} - k x + 2 k$ , where $k$ is a constant, then the value of $k$ is

- 4

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4

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8

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12

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Solution

The correct option is C $8$
$x - 4$ is one of the factor of $x^{2} - k x + 2 k$
Then $x = 4$
Put the value of $x = 4$ in the given equation, we get
$4^{2} - 4 k + 2 k = 0$
$\Rightarrow 16 - 2 k = 0$
$\Rightarrow 16 = 2 k$
$\Rightarrow k = 8$

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