Question

Which of the number(s) below are potential roots of the function q(x) = 6x³ - 19x² - 15x - 28?

1) ±6
2) ±14

Answer 1

Neither ±6 nor ±14 are potential roots of the function q(x) = 6x³ - 19x² - 15x - 28 according to the Rational Root Theorem.

Step-by-step explanation:

To determine which numbers are potential roots of the function q(x) = 6x³ - 19x² - 15x - 28, we can apply the Rational Root Theorem. This theorem suggests that any rational root, expressed in its simplest form as p/q, has a numerator p that is a factor of the constant term (in this case, -28) and a denominator q that is a factor of the leading coefficient (in this case, 6).

Possible values for p are ±6, ±12, ±14, ±28, and possible values for q are ±1, ±2, ±3, ±6. Combining these gives us the potential rational roots: ±1, ±2, ±3, ±4, ±6, ±7, ±9, ±21, ±28. We can see that ±6 and ±14 are not part of these potential roots.

Therefore, neither ±6 nor ±14 are potential roots of the function q(x).