PSAT Math Multiple-Choice Question 175: Answer and Explanation

Question: 175

Which of the following are roots of the equation 3x² - 6 x - 5 =0?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Category: Passport to Advanced Math/Quadratics

Getting to the Answer: The roots of an equation are the same as its solutions. Take a peek at the answer choices—they contain radicals, which tells you that the equation can't be factored. Instead, either complete the square or solve the equation using the quadratic formula, whichever you are most comfortable with. 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. Jot down the values that you'll need: a = 3, b = -6, and c = -5. Then, substitute these values into the quadratic formula and simplify:

This is not one of the answer choices, so simplify the radical. To do this, look for a perfect square that divides into 96 and take its square root. Then, if possible, cancel any factors that are common to the numerator and the denominator:

Choice (D) is correct. Be careful—you can't simplify the answer any further because you cannot divide the square root of 6 by 3.