Advanced Math practice question

Answer: A. There are two solutions: x = 0 and x = 2.

Bring everything to one side and factor: x² − 2x = 0, so x(x − 2) = 0. Either x = 0 or x = 2, and both check: 0 = 0 and 4 = 4. The student divided both sides by x, which silently assumes x ≠ 0 and throws away the solution x = 0.

Why the other answers are wrong

B. The student is correct: x = 2 is the only solution.

Dividing both sides by x gives x = 2 but discards x = 0 — you can't divide by x when x might be 0. Check: 0² = 2(0).

C. The only solution is x = 0.

x = 0 works, but so does x = 2: 2² = 4 = 2(2).

D. The solutions are x = −2 and x = 2.

x = −2 gives 4 on the left and −4 on the right. Those are the solutions of x² = 4, not x² = 2x.

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