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x-axis intersection

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x-axis intersection

by lukaswelker » Thu Apr 17, 2014 8:18 am
Hey Guys

I have a small doubt with the following,

In an (x;y) plane, if y=(x+1)(x-1)2(exponent)+2. At now many point does this line intercept the x-axis?

None : One : Two : Three : Four

Is this a simple as plugging x=0? Sometimes I can't trust easy answers :)

Let me know
Many thanks
Lukas
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by sanju09 » Fri Apr 18, 2014 11:39 pm
lukaswelker wrote:Hey Guys

I have a small doubt with the following,

In an (x;y) plane, if y=(x+1)(x-1)2(exponent)+2. At now many point does this line intercept the x-axis?

None : One : Two : Three : Four

Is this a simple as plugging x=0? Sometimes I can't trust easy answers :)

Let me know
Many thanks
Lukas
Hi Lukas,

First thing first, the given function doesn't represent a line. Rewriting your question according to what I perceived, it reads...

In an (x, y) plane, if y = (x + 1) (x - 1)^2 + 2, then at how many points does the graph of this function would intersect the x-axis?
A. None
B. One
C. Two
D. Three
E. Four

In order to find the x-intercept(s) of a function, we set y = 0, hence

(x + 1) (x - 1)^2 + 2 = 0 or (x + 1) (x - 1)^2 = -2, which means x < -1, where it intersects the x-axis, and if we graph the function on the coordinate axes, we find that it intersects the x-axis just once. There's a calculus approach to answer this question also, which is not fit to be discussed here, and GMAT never forces us to draw graphs of cubic functions, hence it must not be a GMAT query.
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