PSAT Math Multiple-Choice Question 455: Answer and Explanation

Question: 455

Which of the following are the roots of the equation x² + 8x - 3 = 0?

• A.
• B.
• C.
• D.

Correct Answer: A

Explanation:

A

Difficulty: Hard

Strategic Advice: The roots of an equation are the same as its solutions. The equation doesn't factor using reverse FOIL, so you'll have to use a different method to find the solutions. The equation is already written in the form y = ax² + bx + c, and the coefficients are fairly small, so using the quadratic formula is probably the quickest method.

Getting to the Answer: Note the values that you'll need: a = 1, b = 8, and c = -3. Then, substitute these values into the quadratic formula and simplify:

This is not one of the answer choices, which tells you that you'll need to simplify the radical, but before you do, you can eliminate (C) and (D) because the non--radical part of the solutions is not 4. To simplify the radical, look for a perfect square that divides into 76 and take its square root:

This matches (A).