division algorithm.
If one zero of the Polynomial $x^{2} + 3 x + k$ is $2$ find $k .$

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Solution

$f (x) = x^{2} + 3 x + k$
has a zero at $x = 2$
$\Rightarrow f (2) = 0$ (remainder theorem)
$\Rightarrow 4 + 6 + k = 0$
$\Rightarrow k = - 12$

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