The value of $k$ for which $x - k$ is a factor of $x^{3} - k x^{2} + 2 x + k + 4$ is

\frac{- 4}{3}

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- 5

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2

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\frac{6}{7}

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Solution

The correct option is D $\frac{- 4}{3}$
Given $x - k$ is a factor of $f (x) = x^{3} - k x^{2} + 2 x + k + 4$
Therefore, if the divisor is $x - k$
Then $R = f (k) = 0$
$\Rightarrow f (k) = (k)^{3} - k \times {(k)}^{2} + 2 (k) + k + 4$
$\Rightarrow k^{3} - k^{3} + 3 k + 4 = 0$
$\Rightarrow 3 k + 4 = 0$
$\Rightarrow k = - \frac{4}{3}$

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