Question

The real roots of the equation $x^2+5|x|+4=0$ are

• A. $(-1,-4)$
• B. $(\pm 1,\pm 4)$
• C. $(-4,4)$
• D. None of these

Answer 1

Answer: (D)

Given, equation is $x^2+5|x|+4=0$
If $x>0,$ then $|x|=x$
$\therefore$ $x^2+5x+4=0$
$\Rightarrow$ $x^2+4x+x+4=0$
$\Rightarrow$ $(x+4)(x+1)=0$
$\Rightarrow$ $x=-4,-1$ If $x<0,$ then $|x|=-x$
$\therefore$ $x^2-5x+4=0$
$\Rightarrow$ $x^2-4x-x+4=0$
$\Rightarrow$ $(x-4)(x-1)=0$ $\Rightarrow$ $x=4,1$
Hence, no real roots exist.