If one factor of the equation $x^{3} + 7 k x^{2} - 4 k x + 12$ is $(x + 3)$ , then the value of $k$ is

5

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\frac{1}{5}

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- \frac{13}{17}

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- \frac{17}{13}

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Solution

The correct option is B $\frac{1}{5}$
$f (x) = x^{3} + 7 K x^{2} - 4 K x + 12$
$(x + 3)$ is a factor of $f (x)$
So, $f (- 3) = 0$
$- 27 + 63 K + 12 K + 12 = 0$
$75 K = 15$
$= K = \frac{1}{5}$

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