Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. x⁴ + 9

Question

Solve the inequality using a number line and the behavior of the graph at each zero. Write your answer in interval notation. x⁴ + 9 < 10x² A) x $\in$ (-?, -3) $\cup$ (-1, 1) $\cup$ (3, ?) B) x $\in$ (-?, -3) $\cup$ (-1, ?) C) x $\in$ (-?, -1) $\cup$ (3, ?) D) x $\in$ (-3, -1) $\cup$ (1, 3)

Quizplus · Accepted Answer

The inequality simplifies to $x^4 - 10x^2 + 9 < 0$. Factoring gives $(x^2 - 1)(x^2 - 9) < 0$. The zeros are at $x = -3, -1, 1, 3$. Testing intervals between these zeros, the inequality holds for $(-3, -1) \cup (1, 3)$.

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