Question

How many positive real number x satisfy the equation $x^3-3\left|x\right|+2=0?$

• A. $1$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is A $1$

$f\left(x\right)=x^3-3|x|+2=x^3-3x+2$ for $x>0$

$f^{\prime }\left(x\right)=3x^2-3=0$ ,$x=+1,-1$

so at $x=1,f\left(x\right)=0$ and none other value as graph will be touching x-axis and turning back upwards .hence only only one positive real root of $f\left(x\right)$