PSAT Math Multiple-Choice Question 724: Answer and Explanation

Question: 724

What are the values of a in this equation?

3a² - 27a - 108 = 0

• A. -9, -3
• B. 6, -4
• C. 9, 6
• D. 12, -3

Correct Answer: D

Explanation:

(D) You could work backward from the choices if you are so inclined. Algebraically, divide the expression by 3 to simplify:

3a² - 27a - 108 = 0 → a² - 9a - 36 = 0 →

Factor it: (a - 12)(a + 3) = 0

If a = 12, the whole left-hand side equals 0. Similarly, if a = -3, the whole left-hand side equals 0.

Therefore, the solutions are 12, -3.