Advanced MathHardSum of roots after rearranging a product
Advanced Math practice question
If x(x − 3) = 4, what is the sum of all the solutions to the equation?
Answer: 3
Expand and rearrange: x² − 3x − 4 = 0, so (x − 4)(x + 1) = 0. The solutions 4 and −1 sum to 3.
Common wrong answers
- If you answered 4
- 4 is one solution alone (and also the constant on the right).
- If you answered 7
- 7 comes from x − 3 = 4 (treating the product as if x were 1), or from 4 + 3.
- If you answered -4
- −4 is the PRODUCT of the solutions.
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