Question

The number of value(s) of ${}^{\prime }{x}^{\prime }$ which satisfies the equation $x^2+4\left|x\right|+12=0$ is/are

• A. $0$
• B. $1$
• C. $2$
• D. infinite

Answer 1

The correct option is A $0$

Given $x^2+4\left|x\right|+12=0$
$\Rightarrow |x{|}^2+4\left|x\right|+4+8=0$
$\Rightarrow (|x|+2{)}^2+8=0$
Since, $(|x|+2{)}^2>0$ (always)
$\Rightarrow (|x|+2{)}^2+8>0$ (always)
$\therefore x^2+4\left|x\right|+12=0$ has no real solution.