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# On a two dimensional coordinate plane, the curve y=x^2 - x^3

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Intern
Joined: 27 Jun 2010
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On a two dimensional coordinate plane, the curve y=x^2 - x^3 [#permalink]

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20 Sep 2010, 03:32
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Difficulty:

25% (medium)

Question Stats:

67% (01:40) correct 33% (00:54) wrong based on 202 sessions

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On a two dimensional coordinate plane, the curve y=x^2 - x^3 intersects the x-axis at how many points?

A. 0
B. 1
C. 2
D. 3
E. 4

I got the answer as B,

The way i solved the question was to find at how many points a curve touches x axis is by putting y = 0 , when we put y=0 then we get the equation x^2 - x^3 =0

So x^2 = x^3, so cancelling x on both the sides we get x = 1

so the curve touches x axis at x=1 so the answer is B,

But the official answer is C, wat is wrong my method of solving ?
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 35326
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Kudos [?]: 85882 [1] , given: 10258

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20 Sep 2010, 03:39
1
KUDOS
Expert's post
sachinrelan wrote:
On a two dimensional coordinate plane, the curve y=x^2 - x^3 intersects the x-axis at how many points?

A. 0
B. 1
C. 2
D. 3
E. 4

I got the answer as B,

The way i solved the question was to find at how many points a curve touches x axis is by putting y = 0 , when we put y=0 then we get the equation x^2 - x^3 =0

So x^2 = x^3, so cancelling x on both the sides we get x = 1

so the curve touches x axis at x=1 so the answer is B,

But the official answer is C, wat is wrong my method of solving ?

X-intercepts of a graph of a function, in our case $$y=x^2-x^3$$ is the values of $$x$$ for $$y=0$$.

$$y=0$$ --> $$x^2-x^3=0$$ --> $$x^2(1-x)=0$$ --> two solutions: $$x=0$$ and $$x=1$$.

The way you are doing is wrong as when reducing (dividing) the equation $$x^2=x^3$$ by $$x^2$$ you are assuming that $$x\neq{0}$$, so excluding this solution.

Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

Hope it's clear.
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Re: On a two dimensional coordinate plane, the curve y=x^2 - x^3 [#permalink]

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20 Jul 2014, 03:52
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Joined: 09 Sep 2013
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Kudos [?]: 151 [0], given: 0

Re: On a two dimensional coordinate plane, the curve y=x^2 - x^3 [#permalink]

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29 May 2016, 07:21
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: On a two dimensional coordinate plane, the curve y=x^2 - x^3   [#permalink] 29 May 2016, 07:21
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