question_answer

If \[x=3\]is one root of the quadratic equation \[{{x}^{2}}-2kx-6=0\], then find the value of k.

Answer:

Given quadratic equation is,

\[{{x}^{2}}-2kx-6=0\]

\[x=3\] is a root of above equation, then

\[{{(3)}^{2}}-2k(3)-6=0\]

\[9-6k-6=0\]

\[3-6k=0\]

\[3=6k\]

\[\therefore \]      \[k=\frac{3}{6}=\frac{1}{2}\]

\[k=\frac{1}{2}\]