$x ^ { 4 } - 53 x ^ { 2 } + 196

Name: $x ^ { 4 } - 53 x ^ { 2 } + 196 2$ B) $- 7 < x < - 2 \text { or } 2 < x < 7$ C) $- 7 < x < - 2$ D) $- 7 < x < 7$
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Question

$x ^ { 4 } - 53 x ^ { 2 } + 196 < 0$
A) $x < - 2 \text { or } x > 2$
B) $- 7 < x < - 2 \text { or } 2 < x < 7$
C) $- 7 < x < - 2$
D) $- 7 < x < 7$

Quizplus · Accepted Answer

The given inequality can be factored as $(x^2 - 49)(x^2 - 4) < 0$, which simplifies to $(x + 7)(x - 7)(x + 2)(x - 2) < 0$. The roots are $x = -7, -2, 2, 7$. Testing intervals between these roots shows that the inequality holds for $-7 < x < -2$ and $2 < x < 7$.

x4−53x2+196<0x ^ { 4 } - 53 x ^ { 2 } + 196 < 0x4−53x2+196<0

$x ^ { 4 } - 53 x ^ { 2 } + 196 < 0$