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

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On a two dimensional coordinate plane, the curve y=x^2 - x^3 [#permalink] New post 20 Sep 2010, 02:32
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Difficulty:

  25% (low)

Question Stats:

65% (01:38) correct 34% (01:01) wrong based on 52 sessions
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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Re: Curve question [#permalink] New post 20 Sep 2010, 02:39
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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.

Answer: C.

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: Curve question   [#permalink] 20 Sep 2010, 02:39
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On a two dimensional coordinate plane, the curve y=x^2 - x^3

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