PSAT Math Multiple-Choice Question 762: Answer and Explanation

Question: 762

What are the solution(s) to the following ­equation?
5x² – 15x + 10 = 0

• A. 0
• B. 1, 2
• C. 1, 4
• D. 2, 5

Correct Answer: B

Explanation:

(B) First, factor out 5:
5(x² - 3x + 2) = 0
Dividing both sides by 5 leaves you with:
x² - 3x + 2 = 0
This can be factored as:
(x - 2)(x - 1) = 0
Set each factor to 0 to solve for possible x-values:
x - 2 = 0 so x = 2
x -1 = 0 so x = 1
Therefore, the answer is choice (B). Alternatively, you could have used the quadratic formula to solve for possible x-values.