Final answer:
The value of k that makes the discriminant of the quadratic equation kx^2 – 3√2x + 4√2 = 0 equal to 10 is √2 / 4.
Step-by-step explanation:
To find the value of k if the discriminant of the equation kx^2 – 3√2x + 4√2 = 0 is 10, we first need to identify the quadratic equation in the standard form ax^2 + bx + c = 0. In this equation, a = k, b = -3√2, and c = 4√2. The discriminant of a quadratic equation is given by the formula b^2 - 4ac.
So, we set up the equation using the given value of the discriminant:
(-3√2)^2 - 4(k)(4√2) = 10
Solving this equation for k, we get:
9*2 - 16k√2 = 10
18 - 16k√2 = 10
8 = 16k√2
k = 8 / (16√2)
k = 1 / (2√2)
k = √2 / 4