Question

The sum of all real roots of the equation ${|x-2|}^2+|x-2|-2=0$ is

• A. $3$
• B. $12$
• C. $4$
• D. $7$

Answer 1

Answer: (C)

$4$

${|x-2|}^2+|x-2|-2=0$

let $|x-2|=t$ $t\ge 0$ as mod cannot be negative

$t^2+t-2=0t^2+2t-t-2=0t(t+2)-1(t+2)=0(t-1)(t+2)=0t=1or-2$ as $t\ge 0$ therefore $t=1|x-2|=1x-2=1orx-2=-1x=3$

or $x=1$ sum of eqal roots $=3+1=4$