Find the value of $k$ , if $x + k$ is the factor of the polynomial $x^{4} - k^{2} x^{2} + 3 x - 6 k$

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Solution

Consider the given polynomial.

$x^{4} - k^{2} x^{2} + 3 x - 6 k$

Since, $x + k$ is the factor of given polynomial

So, put $x = - k$

Therefore,

${(- k)}^{4} - k^{2} {(- k)}^{2} + 3 (- k) - 6 k = 0$

$k^{4} - k^{4} - 3 k - 6 k = 0$

$- 9 k = 0$

$k = 0$

Hence, the value of $k$ is $0$ .

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