Question

Sum of solutions of the equation $|x{|}^2-|x|+4=2x^2-3|x|+1$ is

• A. $3$
• B. $6$
• C. $0$
• D. none of these

Answer 1

The correct option is C $0$

Case (1),

For $x<0$,

$\left|x\right|=-x$

So, the given equation can be written as

$x^2+x+4=2x^2+3x+1$

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

$x=1,-3$

$x<0$, so $x=-3$ is the only solution in this case.

Case (2),

For $x\ge 0$,

$\left|x\right|=x$

So, the given equation can be written as

$x^2-x+4=2x^2-3x+1$

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

$x=3,-1$

$x\ge 0$, so $x=3$ is the only solution.

Now, Sum of the solutions $=-3+3=0$