If $1$ is the zero of $f (x) = k x^{2} - 3 k x + 3 k - 1$ then the value(s) of $k$ is

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Solution

$f (x) = k x^{2} - 3 k x + 3 k - 1$
If $1$ is the zero of $f (x)$ , then $f (1) = 0$
Thus,
$f (1) = 0$
$=> k (1)^{2} - 3 k (1) + 3 (1) - 1 = 0$
$=> k - 3 k + 3 - 1 = 0$
$=> - 2 k + 2 = 0$
$=> - 2 k = - 2$
$=> k = 1$

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