Final answer:
According to the Rational Root Theorem, -7/8 is a potential rational root of the function f(x) = 24x⁷ + 3x⁶ + 4x³ – x – 28. Therefore, the correct answer is option A.
Step-by-step explanation:
The Rational Root Theorem states that if a polynomial function has a rational root, it can be expressed as a fraction, where the numerator is a factor of the constant term and the denominator is a factor of the leading coefficient. In this case, the potential rational root is -7/8. We need to check which function has -7/8 as a root:
f(x) = 24x⁷ + 3x⁶ + 4x³ – x – 28: To check if -7/8 is a root, we substitute -7/8 for x in the function and check if the result is zero.
If f(-7/8) is equal to zero, then -7/8 is a root.
f(x) = 28x⁷ + 3x⁶ + 4x³ – x – 24
f(x) = 30x⁷ + 3x⁶ + 4x³ – x – 56
f(x) = 56x⁷ + 3x⁶ + 4x³ – x – 30
After evaluating each function at -7/8, we find that f(x) = 24x⁷ + 3x⁶ + 4x³ – x – 28 has -7/8 as a potential rational root.
Therefore, the correct answer is option A.