The real root of the equation $x^{3} - 6x + 9 = 0$ is
- $-6$
- $-9$
- $6$
- $-3$
Reveal answer
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Correct answer
Explanation
Testing the roots, if x = -3, (-3)^3 - 6(-3) + 9 = -27 + 18 + 9 = 0. Thus, -3 is a root.
AI explanation
We can factor the cubic equation x^3 - 6x + 9 = 0 by grouping if we rewrite the middle term as -3x - 3x. This allows us to pull out common factors from the grouped terms: x^3 - 3x - 3x + 9 = x(x^2 - 3) - 3(x - 3). This direct grouping does not factor cleanly, so instead we test the given integer options. Substituting x = -3 into the original equation yields (-3)^3 - 6(-3) + 9 = -27 + 18 + 9 = 0, confirming x = -3 is the real root.