PSAT Math Multiple-Choice Question 456: Answer and Explanation

Question: 456

Which quadratic equation has two real solutions?

• A.
• B.
• C.
• D.

Correct Answer: B

Explanation:

B

Difficulty: Medium

Getting to the Answer: The discriminant is part of the quadratic formula. When the discriminant is negative, there are no real solutions to the equation because the square root of a negative number is not a real number. When the discriminant is 0, there is only one solution. For there to be two real solutions, the discriminant, b² - 4 ac, must be greater than 0.

(A): a = 2, b = 4, c = 2. The discriminant is 4² - 4(2)(2) = 16 - 16 = 0, so this has one real solution. Eliminate (A).

(B): a = 5, b = 5, c = -5. The discriminant is 5² - (4)(5)(-5) = 25 + 100 = 125, so choice (B) must have two real solutions and is correct.

For the record, the discriminant of (C) is -75 and the discriminant of (D) is 0.