Final answer:
To find the value of k for which the function has exactly one root, we use the discriminant of the quadratic equation.
Step-by-step explanation:
Determining the value of k with one root
To find the value of k that gives the function f(x) = kx^2 - 4x + 2 exactly one root, we need to consider the discriminant of the quadratic equation. The quadratic equation has exactly one root when the discriminant is zero. The discriminant, denoted as Δ, is given by the formula Δ = b^2 - 4ac, where a, b, and c are the coefficients of the quadratic equation. In this case, a = k, b = -4, and c = 2. So, the discriminant becomes Δ = (-4)^2 - 4(k)(2).
To have exactly one root, the discriminant must equal zero. So we set Δ = 0 and solve for k:
(-4)^2 - 4(k)(2) = 0
16 - 8k = 0
8k = 16
k = 2.
Therefore, the value of k for which the function has exactly one root is k = 2.
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