Minimum Value of k for Distinct Roots

Consider the equation represented by the function f(x) = 3x^2 - kx + 2, where k is a constant. The function has two distinct real roots when the discriminant of the quadratic equation is positive.

What is the minimum value of k such that the roots of this function remain distinct?

Recall that the discriminant, D, of a quadratic equation ax^2 + bx + c is given by the formula D = b^2 - 4ac. In this case, a = 3, b = -k, and c = 2.

Use the knowledge of the discriminant to find the range of k that keeps the roots of the equation distinct.