Question

Q1. If x = 3 is one root of the quadratic equation x² - 2kx - 6 = 0, then find the value of k.

Solution:
If x = 3 is a root of the quadratic equation x² - 2kx - 6 = 0, then it will satisfy the given equation.
$\Rightarrow$ 3^​2 - 2k(3) - 6 = 0
$\Rightarrow$ K = 12

Answer 1

Dear Student,

$$\begin{gathered} Givenx=3istherootofequation{x}^2-2kx-6=0,whichmeansthatforx=3thevalueof{x}^2-2kx-6willbe0. \\ So,sustitutingx=2intheequation{x}^2-2kx-6,weget \\ {\left(3\right)}^2-2k\left(3\right)-6=0 \\ 9-6k-6=0 \\ -6k+3=0 \\ -6k=-3 \\ \mathit{k}\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}} \end{gathered}$$
Regards