carcass wrote:

What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?

(A) -8

(B) -4

(C) 2

(D) 4

(E) 8

If

x<1, then

|x - 1| = -(x-1)=1-x, so in this case we'll have

x^2 - 4x + 6 = 3-(1-x) -->

x^2-5x+4=0 -->

x=1 or

x=4 --> discard both solutions since neither is in the range

x<1.

If

x\geq{1}, then

|x - 1| = x-1, so in this case we'll have

x^2 - 4x + 6 = 3-(x-1) -->

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

x=1 or

x=2.

Therefore, the product of the roots is 1*2=2.

Answer: C.

We do not need to consider two situation of |x - 1|.

As, x^2 - 4x + 6 = 3 - |x - 1| <=> x^2 - 4x + 3 = - |x - 1| <0 => 1<x (<3) => x^2 - 4x + 3 = x-1 => x^2 - 5x + 4 = 0 => 2 solutions