PSAT Math Multiple-Choice Question 436: Answer and Explanation

Question: 436

What is the absolute value of the difference between the roots of 4x² - 36 = 0?

• A. -6
• B. 0
• C. 3
• D. 6

Correct Answer: D

Explanation:

D

Difficulty: Hard

Category: Classic Quadratics

Getting to the Answer: Notice that this is a difference of squares, so use the formula a² - b² = (a + b)(a - b) with a² = 4x². This means that a = 2x and b² = 36, so b = 6. Therefore, (2x + 6)(2x - 6) = 0. Set both equal to 0 and solve:

Remember that the question asks for the absolute difference of the roots. Think of a number line and count from -3 to 3. The difference is 6. Alternatively, just take the absolute value of the difference between the roots:

Thus, (D) is correct.