Question

For the equation $|x{|}^2+|x|-6=0,$ the sum of the real roots is

• A. $1$
• B. $2$
• C. $0$
• D. None of these

Answer 1

The correct option is C $0$

Equation:- $|x{|}^2+|x|-6=0$

Case $1$:- $x>0$

$x\to x$

$x^2+x-6=0$

$x^2+3x-2x-6=0$

$x(x+3)-2(x+3)=0$

$(x+3)(x-2)=0$

$x=2,-3$ ($-3$ will be neglected because of $x>0$)

Case $2$:-

$x<0$

$x\to -x$

$(-x{)}^2+(-x)-6=0$

$x^2-x-6=0$

$x^2-3x+2x-6=0$

$x(x-3)+2(x-3)=0$

$(x-3)(x-2)=0$

$x=3,2$ ($3$ will be neglected because of $x<0$)

Sum of the Real roots

$\Rightarrow 2+(-2)=0$.