Final answer:
To find the value of x for which (f + g)(x) = 0, we need to solve the quadratic equation (x^2 + 6x + 4) = 0. The solutions to this equation are x = -2 and x = -4. Hence the correct answer is option D
Step-by-step explanation:
To find the value of x for which (f + g)(x) = 0, we need to find the equation (f + g)(x) and solve for x.
Given f(x) = x^2 and g(x) = 6x + 4, the equation (f + g)(x) can be written as (x^2 + 6x + 4) = 0.
Now we need to solve this quadratic equation to find the value(s) of x that make it equal to 0. We can do this using factoring, completing the square, or the quadratic formula.
By factoring or using the quadratic formula, we find that the solutions to the equation are x = -2 and x = -4. Therefore, the correct answer is d. -4.