Question

The number of roots of the equation $|x|=x^2+x-4$ is

• A. 4
• B. 3
• C. 1
• D. 0
• E. 2

Answer 1

Answer: (E)

The given equation is $|x|=x^2+x-4$ If $x\ge 0,x=x^2+x-4$
$\Rightarrow$ $x^2-4=0\Rightarrow x=\pm 2$
$\therefore$ We take, $x=2$ (neglect $x=-2$ ) and
if $x<0$ $-x=x^2-x-4$
$\Rightarrow$ $x^2=4\Rightarrow x=\pm 2$
$\therefore$ We take $x=-2$ (neglect $x=2$ )
Thus, the number of roots of given equation is 2.