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Line intersection x-axis

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Line intersection x-axis [#permalink] New post 03 May 2011, 05:50


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Question Stats:

83% (01:36) correct 17% (03:06) wrong based on 6 sessions
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Re: Line intersection x-axis [#permalink] New post 03 May 2011, 09:19
y = x^2 + (a+b)x + ab is a parabola.Intersecting x axis at two points.
hence we need to find the roots of this equation.

a. a+b = -1 means a= -1 | b = -1 | a=b= -0.5 each etc. Hence not sufficient.

b y = -6 for x = 0

means ab = -6 (substituting in the original quadratic equation.

a= -3,b=1 | a = -6, b = 1 etc. hence not sufficient.

together 1+2

y = x^2 -x -6 = (x-3) * (x + 2) hence two points for X axis.

thus C.

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Re: Line intersection x-axis [#permalink] New post 03 May 2011, 09:21
y=(x+a)(x+b) = x^2+(a+b)x+ab
this is parabola equation. intersects x-axis means y=0

st 1--> a+b = -1
x^2-x+ab=0 cannot solve the equation; not sufficient

st 2--> graph intersects y-axis at -6
i.e. ab = -6
x^2+(a+b)-6=0 cannot solve the eq, not sufficient.

Both together, x^2-x-6=0
Solving gives x = -2 or x=3

Hence C.
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Re: Line intersection x-axis [#permalink] New post 03 May 2011, 17:33
Expert's post
udaymathapati wrote:

At what two points does the graph of y = (x+a)(x+b) intersect the x axis?

You don't need to worry what the equation represents. Just think, what does 'intersection with x axis' imply? It means the y co-ordinate is 0.

0 = (x+a)(x+b)
or x = -a or -b
Hence the graph must intersect the x axis at points (-a, 0) and (-b, 0). We need the values of a and b now.

Statement 1: a + b = -1
Two variables, only one equation. Not sufficient.

Statement 2: Graph intersects the y axis at (0, -6).
At y axis, x = 0. This means when x = 0, y co-ordinate is -6.
Put these values in y = (x+a)(x+b) to get -6 = ab.
Again, two variables, one equation. Not sufficient alone.

Using both statements, we have two variables and two different equations so we will be able to find the values of a and b. It doesn't matter which is 'a' and which is 'b'. We find that the two of them are -3 and 2. Since we need the points (-a, 0) and (-b, 0), the required points are (3, 0) and (-2, 0). Sufficient.

Answer (C).

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Re: Line intersection x-axis   [#permalink] 03 May 2011, 17:33
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