If $x = 3$ is one root of the quadratic equation $x^{2}-2kx-6=0$ , then find the value of $k$.
Given: $x = 3$ is one root of the quadratic equation $x^{2}-2kx-6=0$
To do: To find the value of k.
Solution:
The given equation, $x^{2}-2kx-6=0$
If $x=3$, then it will satisfy the equation,
$\Rightarrow (3)^{2}-2k(3)-6=0$
$\Rightarrow9-6k-6=0$
$\Rightarrow3-6k=0$
$\Rightarrow6k=3$
$\Rightarrow k=\frac{3}{6}$
$\Rightarrow k=\frac{1}{2}$
Therefore the value of $k=\frac{1}{2}$
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