Question

If $A=\{x\in R:x^2-5|x|+6=0\}$, then $n\left(A\right)=$ ________.

• A. $2$
• B. $0$
• C. $1$
• D. $4$

Answer 1

The correct option is D $4$

The question indirectly wants to know the number of real roots for the given quadratic equation,

Let's solve for roots,

$x^2-5|x|+6=0\to (|x|-2)(|x|-3)=0$ which gives $x=\{2,-2,3,-3\}$

Thus $n\left(A\right)=4$