If A = {x in mathbb{R} : x^2 + 5|x| + 6 = 0}, | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We are given the set $A = \{x \in \mathbb{R} : x^2 + 5|x| + 6 = 0\}$.Since $x^2 = |x|^2$,the equation can be written as $|x|^2 + 5|x| + 6 = 0$.Let

Vedclass · Accepted Answer

$0$

Vedclass · Answer

(A) We are given the set $A = \{x \in \mathbb{R} : x^2 + 5|x| + 6 = 0\}$.Since $x^2 = |x|^2$,the equation can be written as $|x|^2 + 5|x| + 6 = 0$.Let $|x| = t$,where $t \ge 0$. The equation becomes $t^2 + 5t + 6 = 0$.Factoring the quadratic,we get $(t + 2)(t + 3) = 0$.This gives $t = -2$ or $t = -3$.Since $t = |x|$ must be non-negative $(t \ge 0)$,there are no real values of $x$ that satisfy these conditions.Therefore,the set $A$ is an empty set,i.e.,$A = \emptyset$.Thus,the number of elements in $A$ is $n(A) = 0$.

If $A = \{x \in \mathbb{R} : x^2 + 5|x| + 6 = 0\}$,then $n(A) = $

Similar Questions

Determine whether the following set is finite or infinite:
$\{1, 2, 3, \ldots\}$

In each of the following,determine whether the statement is true or false. If it is true,prove it. If it is false,give a counterexample.
If $A \not\subset B$ and $B \not\subset C$,then $A \not\subset C$.

Let $A = \{1, 2, 3, 4, 5, 6\}$. Insert the appropriate symbol $\in$ or $\notin$ in the blank space:
$8 \dots A$

Find the union of each of the following pairs of sets:
$A = \{1, 2, 3\}, B = \varnothing$

How many elements does $P(A)$ have,if $A = \varnothing$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module