Question

For the equation $\left|x^2\right|+|x|-6=0$, the roots are

• A. real and equal
• B. real with sum 0
• C. real with sum 1
• D. real with product 0

Answer 1

Answer: (B)

For, $x<0,|x|=-x$
$\therefore$ equation is
$x^2-x-6=0$
$\Rightarrow x=-2,3$
$\because x<0$
$\therefore x=-2$ is the solution
For, $x\ge 0,|x|=x$,
$\therefore$ equation is
$x^2+x-6=0$
$\Rightarrow x=2,-3$
$\because x\ge 0$
$\therefore x=2$ is the solution.
Hence, $x=2,-2$ are the solutions and their sum is zero.