Solve the inequality. Write the solution set in interval notation.
-$$\left| x ^ { 4 } + 6 x ^ { 2 } + 9 \right|

Question

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

Quizplus · Accepted Answer

The expression inside the absolute value, $x^4 + 6x^2 + 9$, is a sum of squares and is always non-negative. Specifically, it can be factored as $(x^2 + 3)^2$, which is always greater than or equal to 0. Since the absolute value of a non-negative number cannot be less than 0, there are no solutions to the inequality. Therefore, the solution set is the empty set, denoted by $\varnothing$.

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

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