PSAT Math Multiple-Choice Question 443: Answer and Explanation

Question: 443

If a quadratic function f(x) has solutions a and b such that a < 0, b > 0, and | b | > | a |, which of the following could be equal to f(x)?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Hard

Getting to the Answer: Set each answer choice equal to zero and factor to determine which one meets the criteria posed in the question: the solutions must have different signs and the positive solution must have a greater absolute value than the negative solution.

(A):

The solutions are 2 and -3. They have different signs, but the negative solution has the greater absolute value. Eliminate (A).

(B):

This time, the solutions are -2 and 3, so the criteria are met. (B) is correct.

For the record:

(C):

This has the same solutions as (A). Eliminate (C).

(D):

The solutions are 0 and 2. Eliminate (D) and confirm that (B) is correct.