x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0, then other root is :

1. -1

2. 3

3. -3

4. -4

Since, x = 3 is a solution of the quadratic equation (k + 2)x² - kx + 6 = 0, thus substituting x = 3 in the equation, we get,

⇒ (k + 2).(3)² - k.(3) + 6

⇒ 9(k + 2) - 3k + 6 = 0

⇒ 9k + 18 - 3k + 6 = 0

⇒ 6k + 24 = 0

⇒ 6k = -24

⇒ k = -4.

Equation : (-4 + 2)x² - (-4)x + 6 = 0

⇒ -2x² + 4x + 6 = 0

⇒ 2x² - 4x - 6 = 0

Solving the equation :

⇒ 2x² - 6x + 2x - 6 = 0

⇒ 2x(x - 3) + 2(x - 3) = 0

⇒ (x - 3)(2x + 2) = 0

⇒ x - 3 = 0 or 2x + 2 = 0

⇒ x = 3 or 2x = -2

⇒ x = 3 or x = -1.

Hence, the other root of the equation = -1.