Question

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

Answer 1

$x = 3 \\ {x}^{2} - 2kx - 6 = 0 \\ {3}^{2} - 2 (3)k - 6 = 0 \\ 9 - 6k - 6 = 0 \\ 3 - 6k = 0 \\ - 6k = - 3 \\ 6k = 3 \\ k = \frac{3}{6} \\ k = \frac{1}{2}$
Heyy friend your answer is here

Answer 2

We know that,

$\alpha + \beta = \frac{- b}{a} \\ \alpha \beta = \frac{c}{a}$
Given,
$- 6 = \frac{c}{a} \\ \alpha \beta = - 6 \\ 3 \beta = - 6 \\ \beta = - 2$
Now,
$\alpha + \beta = \frac{ - b}{a} \\ 3 + ( - 2) = \frac{ - 2k}{1} \\ 1 = - 2k \\ k = - \frac{1}{2}$