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20 Sep 2010, 03:32
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C
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Difficulty:
25%
(medium)
Question Stats:
68% (01:04) correct
32%
(01:07)
wrong
based on 364
sessions
History
Date
Time
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Not Attempted Yet
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
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 ?
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 ?
20 Sep 2010, 03:39
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sachinrelan
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.
29 Oct 2016, 02:12
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Bunuel, in mgmat tells us that the number of times a parabola touches the x axis can be figured out calucating the value of b^2-4ac for any equation in the form of ax^2+bx+c. can that concept be applied for the equaiton of this question - x^2-x^3? Let me know your thoughts, thank you.
