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geomatrace
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Say I have the equation: x^2 = -2x I am tempted to simply Updated on: 25 Sep 2007, 20:07
Originally posted by geomatrace on 25 Sep 2007, 19:38.
Last edited by geomatrace on 25 Sep 2007, 20:07, edited 1 time in total.
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Say I have the equation: x^2 = -2x

I am tempted to simply divide each side by x, which results in: x = -2

But I understand that to be an incomplete solution. If I simplify differently, I wind up with:

x^2 = -2x
x^2 + 2x = 0
x(x + 2) = 0

Hence x = 0, -2.

Can anyone please explain this to me conceptually? How can I avoid repeating this mistake? Should I ALWAYS try to set up exponential equations by putting 0 (zero) on one side and all other terms on the other side, i.e.

POLYNOMIAL = 0

?

Thanks,
GeoMATrace



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GMATBLACKBELT
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Say I have the equation: x^2 = -2x I am tempted to simply 25 Sep 2007, 20:01
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geomatrace
Say I have the equation: x^2 = -2x

I am tempted to simply divide each side by x, which results in: x = -2

But I understand that to be an incomplete solution. If I simply differently, I wind up with:

x^2 = -2x
x^2 + 2x = 0
x(x + 2) = 0

Hence x = 0, -2.

Can anyone please explain this to me conceptually? How can I avoid repeating this mistake? Should I ALWAYS try to set up exponential equations by putting 0 (zero) on one side and all other terms on the other side, i.e.

POLYNOMIAL = 0

?

Thanks,
GeoMATrace
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Yes. u should b/c when u use the method u first showed, then ur eliminating a value of X.
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done_gre_now_gmat
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Say I have the equation: x^2 = -2x I am tempted to simply 25 Sep 2007, 20:11
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geomatrace
Say I have the equation: x^2 = -2x

I am tempted to simply divide each side by x, which results in: x = -2

But I understand that to be an incomplete solution. If I simply differently, I wind up with:

x^2 = -2x
x^2 + 2x = 0
x(x + 2) = 0

Hence x = 0, -2.

Can anyone please explain this to me conceptually? How can I avoid repeating this mistake? Should I ALWAYS try to set up exponential equations by putting 0 (zero) on one side and all other terms on the other side, i.e.

POLYNOMIAL = 0

?

Thanks,
GeoMATrace
Show more


In short the answer is YES, you have to equate a polynomial to a zero, by bringing all the terms to LHS. Solving by bringing all the variables in a polynomial equation to the LHS allows you to extract all the "real" roots of the equation, if they exist. Now, there are equations like x^2+1 which does not have real roots but that's besides the point.

By solving equations the way you are solving you are not guaranteed to find all the roots of the equation. Clearly from you own example, you have seen that by using your method "0" is not seen as one of the roots of the equation.

HTH



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!