Solve the problem.
-$x ^ { 4 }

Question

Solve the problem.
-$x ^ { 4 } < 81 x ^ { 2 }$
A) $( - \infty , - 9 )$ or $( 9 , \infty )$
B) $( - 9,0 )$ or $( 9 , \infty )$
C) $( - \infty , - 9 )$ or $( 0,9 )$
D) $( - 9,0 )$ or $( 0,9 )$

Quizplus · Accepted Answer

First, rearrange the inequality to $x^4 - 81x^2 < 0$, which simplifies to $x^2(x^2 - 81) < 0$. Factoring further gives $x^2(x + 9)(x - 9) < 0$. The roots are $x = 0$, $x = -9$, and $x = 9$. Plotting these on a number line and testing intervals shows that the inequality is satisfied for $x$ in the intervals $(-9, 0)$ and $(0, 9)$.

Solve the Problem x4<81x2x ^ { 4 } < 81 x ^ { 2 }x4<81x2

Solve the Problem $x ^ { 4 } < 81 x ^ { 2 }$