Answer:

k = 1/2√2

Step-by-step explanation:

Discriminant of a quadratic equation ax² + bx + c = 0 is D = b² - 4ac
Here, a = k ; b = -3√2 ; c = 4√2 and D is given as 10.

Substituting the respective values :

10 = (-3√2)² - 4(k)(4√2)

or 10 = 18 - 16√2*k

or 16√2*k = 8

or √2*k = 1/2

or k = 1/2√2