Advanced MathEasy–MediumGap between the roots' constants
Advanced Math practice question
The expression x² + 10x + 21 factors as (x + a)(x + b), where a and b are constants with a < b. What is the value of b − a?
Answer: 4
The factors are (x + 3)(x + 7): the constants multiply to 21 and add to 10. Then b − a = 7 − 3 = 4.
Common wrong answers
- If you answered 2
- The pair is 3 and 7 — not 4 and 6, whose product would be 24.
- If you answered 10
- 10 is a + b (the x-coefficient), not the difference.
- If you answered 21
- 21 is a · b (the constant term).
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