Final answer:
To find the values of x for which the function k(x) equals zero, we need to solve the equation 3x^2 - 19x - 14 = 0. The values of x that satisfy this equation are 2 and -7/3.
Step-by-step explanation:
To find the values of x for which the function k(x) equals zero, we need to solve the equation 3x^2 - 19x - 14 = 0. To do this, we can either factor the equation or use the quadratic formula.
Factoring the equation, we find (x - 2)(3x + 7) = 0. Thus, x - 2 = 0 or 3x + 7 = 0. Solving these equations, we get x = 2 or x = -7/3. So, the values of x for which k(x) equals zero are 2 and -7/3.