Advanced MathVery hardZeros of a cubic
Advanced Math practice question
The function g is defined by g(x) = x³ − 4x. How many distinct values of x satisfy g(x) = 0?
- A. 3Correct
- B. 1
- C. 2
- D. 0
Answer: A. 3
Factor: x(x² − 4) = x(x − 2)(x + 2), so the zeros are 0, 2, and −2 — three distinct values.
Why the other answers are wrong
- B. 1
- 1 counts only x = 0, missing the factor x² − 4.
- C. 2
- 2 counts ±2 but forgets x = 0 from the factored-out x.
- D. 0
- 0 would mean the graph never touches the x-axis; every odd-degree polynomial has at least one real zero.
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