Final answer:
No given function has real zeros at both x = -8 and x = -5; the function with these zeros would be x² + 13x + 40, but this is not one of the options presented, so the answer is 'None of the above'.
Step-by-step explanation:
To find the function with real zeros at x = -8 and x = -5, you can use these zeros to create factors of the function. The factors associated with these zeros would be (x + 8) and (x + 5). When these two factors are multiplied together, they create a quadratic equation in the form of ax² + bx + c = 0.
To find which function matches with the given zeros, expand these factors:
(x + 8)(x + 5) = x² + 5x + 8x + 40
= x² + 13x + 40
The correct quadratic function that has real zeros at x = -8 and x = -5 is g(x) = x² + 13x + 40. However, this option is not listed. Therefore, the correct answer is D) None of the above.