Question

The number of real solutions of the equation ${|x|}^2+5|x|+4=0$ is

• A. $0$
• B. $1$
• C. $2$
• D. $3$
• E. $4$

Answer 1

Answer: (A)

$0$

${\left|x\right|}^2+5\left|x\right|+4=0$

$Let\left|x\right|=y$

$y^2+5y+4=0$

$\Rightarrow y^2+4y+y+4=0$

$\Rightarrow y\left(y+4\right)+1\left(y+4\right)=0$

$\Rightarrow \left(y+4\right)\left(y+1\right)=0$

$\Rightarrow y=-1,-4$

$\Rightarrow \left|x\right|=-1,\left|x\right|=-4$

which is not possible

Hence no real solution exists.