Final answer:
Yuri must evaluate q(a) to determine if x = a is a root. If q(a) is non-zero, then x = a is not a root of the function q(x). The specific value of a is required for further calculations.
Step-by-step explanation:
To explain to Yuri why x = a cannot be a root of the function q(x) = 6x³ - 19x² - 15x - 28, we must evaluate q(a). If q(a) = 0, then x = a would indeed be a root. However, if q(a) ≠ 0, then x = a is not a root of the function. The options provided by Yuri suggest evaluating whether q(a) is positive, negative, or non-zero to determine if x = a can be a root.
The correct answer to Yuri's question depends on the value of q(a). We need to substitute the value of a into the function q(x) and calculate the result. If after the substitution q(a) results in any number other than zero, then option d) q(a) ≠ 0 is the correct answer because it shows that x = a is not a root.
Without the specific value of a, we cannot determine whether q(a) is greater than, less than, or equal to zero; therefore, we cannot select options a), b), or c) as the direct answer. Only plagiarism free content is provided here, and no calculation step can be completed without the value of a.