Advanced MathMediumSum of the numbers satisfying a quadratic condition
Advanced Math practice question
A number is 6 less than its square. What is the sum of all such numbers?
Answer: 1
Let the number be n: n = n² − 6, so n² − n − 6 = 0 → (n − 3)(n + 2) = 0. The numbers are 3 and −2, and their sum is 1.
Common wrong answers
- If you answered 3
- 3 is one of the numbers; −2 also works, and the question asks for their sum.
- If you answered 5
- 5 is 3 − (−2), the difference.
- If you answered -6
- −6 is the product of 3 and −2.
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