What are the roots of the polynomial x² - x - 6?

To find the roots of the polynomial x² - x - 6, we can factor it. We are looking for two numbers that multiply to -6 (the constant term) and add to -1 (the coefficient of the linear term). The numbers 3 and -2 satisfy these conditions, as 3 * (-2) = -6 and 3 + (-2) = 1.

Therefore, we can express the polynomial as (x - 3)(x + 2). Setting each factor equal to zero gives us the two roots:

1. x - 3 = 0 → x = 3
2. x + 2 = 0 → x = -2

This means the roots of the polynomial x² - x - 6 are indeed x = 3 and x = -2. Thus, this choice accurately represents the solution to the equation. These roots indicate the values of x where the polynomial equals zero, confirming that the answer is valid.