PSAT Math Multiple-Choice Question 454: Answer and Explanation

Question: 454

Which of the following are the real values of x that satisfy the equation ?

• A. 3 and -2
• B.
• C. 0
• D. The equation has no real solutions.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Strategic Advice: When factoring isn't easy, try a different approach. If you were able to use a calculator, the fastest method might be to graph the function. Because this is a no-calculator question, use the quadratic formula.

Getting to the Answer: The first step in answering the question is to manipulate the equation so that it's equal to 0:

Now, solve using the quadratic formula:

When you solve using the quadratic formula, you get a negative number under the square root, which means there are no real solutions. The correct answer is (D).

Although you couldn't use a graphing calculator for this question, for the record, if you could graph the function, you'd see that the graph does not cross the x-axis, which means no real solutions:

(D) is indeed correct.