Final answer:
The atroes of the function f(x) = x⁴ + 8x³ + 17x² - 2x - 24 cannot be determined easily by inspection or factorization.
Step-by-step explanation:
The given function is f(x) = x⁴ + 8x³ + 17x² - 2x - 24. To find the atroes (zeros) of this function, we set f(x) equal to zero:
x⁴ + 8x³ + 17x² - 2x - 24 = 0
We can use the quadratic formula to solve this equation. However, this equation is not a quadratic equation. It is a quartic equation (degree 4). To solve quartic equations, we can use numerical methods or factorization. In this case, none of the roots can be easily determined by inspection or factorization. Therefore, we can conclude that the provided options do not correspond to the atroes of the function.