Question

The sum of all roots of the equations ${|x-1|}^2-5|x-1|+6=0$ is

• A. 5
• B. 4
• C. 2
• D. 6

Answer 1

Answer: (B)

4

let $|x-1|$=$a$

Now the above given equations becomes as follows:

$a^2-5a+6=0$

$⟹(a-3)(a-2)=0$

$⟹a=3$ or $a=2$

Both of these values of acceptable since both are positive.

Resubstituting a we get:

$|x-1|=2$ or $|x-1|=3$

$⟹x-1=\pm 2$ or $x-1=\pm 3$

So values possible for x are: 3,-1,4,-2

So sum of all the roots is 4.