16Hit1600
Advanced MathHardSum of all real solutions of a cubic

Advanced Math practice question

If x³ = 9x, what is the sum of all real solutions to the equation?

Answer: 0

Move everything to one side and factor: x³ − 9x = x(x² − 9) = x(x − 3)(x + 3) = 0. The solutions are 0, 3 and −3, which sum to 0. (Dividing by x would have lost the solution x = 0.)

Common wrong answers

If you answered 3
3 is only the positive solution; −3 and 0 are solutions too.
If you answered 6
6 adds 3 and 3, missing that one root is −3.
If you answered 9
9 is the coefficient in the equation, not a sum of solutions.

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