Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| 0$$
A) $\varnothing$
B) $( - 3,3 )$
C) $( - \infty , - 3 ) \cup ( 3 , \infty )$
D) $( - \infty , \infty )$

Question

Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0$$
A) $\varnothing$
B) $( - 3,3 )$
C) $( - \infty , - 3 ) \cup ( 3 , \infty )$
D) $( - \infty , \infty )$

Quizplus · Accepted Answer

The expression inside the absolute value, $x^4 + 6x^2 + 9$, is a sum of squares and is always positive for all real x, except it equals 0 when $x^2 = -3$, which has no real solutions. Therefore, the absolute value of this expression is always greater than 0 for all real numbers, making the solution set all real numbers, or $( - \infty , \infty )$.

Solve the Inequality ∣x4+6x2+9∣>0\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0​x4+6x2+9​>0

Solve the Inequality $\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right| > 0$