If one root of the equation 3x*x - kx - 2=0 is 2, find the value of k. Also find the other root.

Given, one root of the equation 3x² - kx - 2=0 is 2.

So, we have:

3(2)² - k(2) - 2=0

12 - 2k - 2 = 0

10 = 2k

k = 5

 

Now, the quadratic equation becomes:

3x² - 5x - 2=0

3x² - 6x + x - 2=0

3x(x - 2) + 1(x - 2) = 0

(x - 2)(3x + 1) = 0

x = 2, -1/3

 

Thus, the other root is -1/3.