Question

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

Answer 1

given it's one root of the equation x² - 2kx - 6 = 0

one of its root x = 3
for finding the value of k put the value of x in this equation.

(3)² - 2k(3) - 6 = 0

9 - 6k - 6 = 0

6k = 3

k = 3/6

k = 1/2

hence,the value of k = 1/2


$\bold{ VERIFICATION:-}$

x² - 2(1/2)x - 6 = 0

x² - x - 6 = 0

x² - 3x + 2x - 6 = 0

x(x - 3) + 2(x - 3) = 0

(x + 2)(x - 3) = 0

x = 3 , x = -2

Answer 2

Value of k is 1/2.

Given

To find the value of k.

x=3 is the root of $x^{2} - 2kx-6 =0$.

Hence, the given quadratic equation is $x^{2} - 2kx-6 =0$

Where, x = 3

Now, substituting "x = 3" in the given quadratic equation.

                       $x^{2} - 2kx-6 =0$

By substituting the x value and solving it, following steps are generated

                       $3^2 - 2k(3) - 6 =0$  

                       $9- 6k - 6 =0$           ( 2×3×k = 6k )

                             $3-6k=0$           ( 9-6 = 3 )

                                $-6k = -3$          

                                    $6k=3$        

                                      $k = \frac{3}{6}$

                                      $k = \frac{1}{2}$        

Therefore, value of k is $\frac{1}{2}$.      

To learn more...

1. brainly.in/question/3098309

2. brainly.in/question/3116714