What is the product of all the roots on the equation (x - 2)^2 =

Question

What is the product of all the roots on the equation (x - 2)^2 = |x - 2|?

A. -3
B. -2
C. 2
D. 3
E. 6

VivekSri · Answer

OA is E

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WNBIB · Answer

Here is a logical approach to this question.
You see that the square of some number is equal to the absolute value of that number. This can only be attainable when that number is either 0 or 1. 
x - 2 = 0 or x-2 = 1
x = 2 or x = 3
Product of roots is 6

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btsaami · Answer

What's the Official solution for this?

piermacabj · Answer

If the square of a number is the number itself then the only possible solutions are 0 or 1

We know, by av properties, that |a|^2 = a^2

Therefore;

|x - 2|^2 = (x - 2)^2

So we end with the following equation:

|x - 2|^2 = |x - 2|

The number |x - 2| has to be either 1 or 0 so:

|x - 2| = 0

x = 2

|x - 2| = 1

x = 1 
x = 3

The roots are 1, 2 and 3, which product is 6
 Ans E

What is the product of all the roots on the equation (x - 2)^2 =

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What is the product of all the roots on the equation (x - 2)^2 =

Prep Toolkit

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