Determine the range of values for $x^2$ under the condition that $(x^2 + 5)(x^2 - 3) < 0$ .

Answer Choices

Correct answer marked below

-5 < x^2 < 3

-1 ≤ x^2 ≤ 3

0 ≤ x^2 < 3

Correct

1 < x^2 < 3

-∞ < x < 3

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Explanation

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Official Explanation

Official

To find the range of values for

x^2

such that (

x^2

+5)(

x^2

-3)<0, we analyze the inequality. The expression will be negative when one factor is positive and the other is negative. The critical points are found by setting each factor to zero: [m]x^2 +…

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What this question tests

What it tests

Your ability to solve and combine linear inequalities and reason about ranges of values.

Common trap

Failing to flip the inequality sign when multiplying or dividing by a negative, or missing an inclusive/exclusive endpoint.

Determine the range of values for x2x^2x2 under the condition that (x2+5)(x2−3)<0(x^2 + 5)(x^2 - 3) < 0(x2+5)(x2−3)<0.