Which of the following expressions CANNOT be equal to 0 when x^2 − 2x

x^2 − 2x = 3
Rearrange to get: x^2 − 2x - 3 = 0
Factor: (x - 3)(x + 1) = 0
Conclusion: EITHER (x - 3) = 0 OR (x + 1) = 0
The correct answer will be the one in which we CANNOT draw either of these conclusions.

IMPORTANT: To answer this question, we must start checking each answer choice. Given that most people start with A and work their way down, where is the sneakiest place to place the correct answer? Near the bottom. So, in these cases, I suggest that you start with E and work your way UP. For more on this strategy, see my article: https://www.gmatprepnow.com/articles/han ... -questions

E. Can x^2 − 9 = 0?
Factor to get (x + 3)(x - 3) = 0
So, (x + 3) = 0 or (x - 3) = 0
ELIMINATE E

D. Can x^2 − 7x + 6 = 0
Factor to get (x - 1)(x - 6) = 0
So, (x - 1) = 0 or (x - 6) = 0
Since we cannot conclude that (x - 3) = 0 or (x + 1) = 0, the correct answer must be D

Cheers,
Brent

Which of the following expressions CANNOT be equal to 0 when x^2 − 2x = 3?
x^2 − 2x = 3
x^2 − 2x - 3= 0
x=-1 or x=3

All other choices result in a possibility of 0 when you plug in -1 or 3 for x
D. x^2 − 7x + 6

Firstly, I started solving this way:
x^2 − 2x = 3
x (x - 2) = 3
Either x = 3,
or
x - 2 = 3
=> x = 5

While noticing that putting 5 in the original equation (25 - 10) doesn't equal to 3, l realized l could put all values in one side x^2 − 2x − 3 = 0 to derive at x = 3 or -1, and then answer the question.

l was wondering what's wrong with the approach l started with. Could someone clarify please?

Thank you.
Regards.

Hi Ranaazad,
This way is a bit faulty.

When you say x (x - 2) = 3 then x = 3/(x-2) or (x - 2) = 3/x.

What you're ignoring is that you have integer 3 at the right-hand side, not ZERO.

x^2 − 2x = 3
=>x^2 − 2x - 3 = 0
=>x^2 − 3x + x - 3 = 0
=>x(x − 3) + 1(x - 3) = 0
=>(x − 3)(x + 1) = 0
therefore
x=-1 or 3
Check with options keeping x=-1 or 3

A. x^2 − 6x + 9 => will yield 0 when x=3
B. x^2 − 4x + 3 => will yield 0 when x=3
C. x^2 − x − 2 => will yield 0 when x=-1
D. x^2 − 7x + 6 => will not yield 0 when x=-1 or 3 Hence answer D
E. x^2 − 9 => will yield 0 when x=3