Two quadratic equations, x² - 5x + 6 = 0 and 2x² - kx + 6 = 0, have one common root. What is the possible value of k?

Correct option is C

Given:

Two equations:

​$$x^2 - 5x + 6 = 0$$​​

​$$2x^2 - kx + 6 = 0$$​​

They have one common root.

Concept Used:

If two quadratic equations share one root, then that root satisfies both equations.

Solution:

​$$x^2 - 5x + 6 = 0$$​​

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

x = 2, 3

For common root 2:

Substituting in second equation:

(2)² - 2k + 6 = 0

8 - 2k + 6 = 0

14 - 2k = 0

k = 7

For  common root = 3:

(3)² - 3k + 6 = 0

18 - 3k + 6 = 0

24 - 3k = 0

k = 8

Thus, Possible values of k: 7 or 8