If $(x - 1)$ is a factor of $k x^{3} - 4 k x^{2} + 4 k x - 1$ , the the value of $k$ is

1

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Solution

The correct option is C $1$
Since $(x - 1)$ is a factor of $k x^{3} - 4 k x^{2} + 4 k x - 1$
$(x - 1)$ must be the zeros of the polynomial.
Putting $x = 1$ in the equation we get,
$k {(1)}^{3} - 4 k {(1)}^{2} + 4 k (1) - 1 = 0$
$=> k - 4 k + 4 k - 1 = 0$
$=> k = 1$

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