Determine the roots of the equation x² - 9 = 0.

• A. 1, -1
• B. 3, -3
• C. 2, -2
• D. 4, -4

Answer: (B)

To solve the equation x² - 9 = 0, we start by recognizing that this is a difference of squares. The equation can be factored as (x - 3)(x + 3) = 0.

Setting each factor equal to zero gives us the possible solutions.

1. From the first factor (x - 3) = 0, we find x = 3.

2. From the second factor (x + 3) = 0, we find x = -3.

Thus, the roots of the equation are 3 and -3. This indicates that the equation has two solutions located on the number line, one positive and one negative, effectively reflecting the symmetry of the values around zero.

In this context, the correct answer aligns with these identified roots perfectly. The other options listed do not satisfy the original equation upon substitution and do not reflect the roots derived from the equation. Understanding the concept of factoring and the difference of squares is key in arriving at the correct answer.