If $3$ is the zero of $f (x) = x^{4} - x^{3} - 8 x^{2} + k x + 12$ then the value of $k$ is equal to

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Solution

$f (x) = f (x) = x^{4} - x^{3} - 8 x^{2} + k x + 12$
If $3$ is the zero of $f (x)$ ,then,
$f (3) = 0$
$= 3^{4} - 3^{3} - 8 (3)^{2} + k (3) + 12$
$= 81 - 27 - 72 + 3 k + 12$
$= 93 - 99 + 3 k$
$=> 3 k = 6$
$=> k = 2$

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