Solve the polynomial inequality.
-$$x ^ { 4 } - 145 x ^ { 2 } + 5184

Question

Solve the polynomial inequality.
-$$x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0$$
A) $( - 9,9 )$
B) $( - \infty , - 8 ) \cup ( 8 , \infty )$
C) $( - 9 , - 8 ) \cup ( 8,9 )$
D) $( - 9 , - 8 ) \cap ( 8,9 )$

Quizplus · Accepted Answer

The inequality can be factored as $(x^2 - 81)(x^2 - 64) < 0$. Solving $x^2 - 81 = 0$ gives $x = \pm 9$ and solving $x^2 - 64 = 0$ gives $x = \pm 8$. The intervals to test are $(-9, -8)$, $(-8, 8)$, and $(8, 9)$. The inequality holds in $(-9, -8)$ and $(8, 9)$.

Solve the Polynomial Inequality x4−145x2+5184<0x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0x4−145x2+5184<0

Solve the Polynomial Inequality $x ^ { 4 } - 145 x ^ { 2 } + 5184 < 0$