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# In the xy-plane at what points does the graph of

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In the xy-plane at what points does the graph of [#permalink]  17 Jan 2010, 13:28
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75% (02:24) correct 25% (02:07) wrong based on 4 sessions
In the xy-plane at what points does the graph of y=(x+a)(x+b) intersect the x axis?

(1) a+b= -1
(2) The graph intersects the y-axis at(0,-6)

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Re: How to solve? [#permalink]  17 Jan 2010, 13:57
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samrand wrote:
In the xy-plane at what point does the graph of y=(x+a)(x+b) intersect the x axis?
1. a+b= -1
2.The graph intersects the y-axis at(0,-6)

X-intercepts of the function f(x) or in our case the function (graph) y=(x+a)(x+b) is the value(s) of x for y=0. So basically the question asks to find the roots of quadratic equation (x+a)(x+b)=0.

(x+a)(x+b)=0 --> x^2+bx+ax+ab=0 --> x^2+(a+b)x+ab=0.

Statement (1) gives the value of a+b, but we don't know the value of ab to solve the equation.

Statement (2) tells us the point of y-intercept, or the value of y when x=0 --> y=(x+a)(x+b)=(0+a)(0+b)=ab=-6. We know the value of ab but we don't know the value of a+b to solve the equation.

Together we know the values of both a+b and ab, hence we can solve the quadratic equation, which will be the x-intercepts of the given graph.

Hope it's clear.
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Re: How to solve? [#permalink]  22 Jun 2010, 12:23
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Re: coordinate geometry - DS [#permalink]  27 Jun 2010, 04:58
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i think that the answer is (C)

since it is a quadratic equation, it will cross the x axis at 2 points

at y =0(x-axis), we get, x = -a,-b
now we need to find the values of a and b to get the 2points at which it intersects x-axis, the 2 points being (-a,0)and (-b,0)

statement (1) gives us an equation which by itself is useless but when used with statement(2), it helps. statement 2 tells us that a*b = -6. this we get by putting the respective values of x and y in statement 2.

now, we have 2 equations, one frm statement(1)and the other(a*b = -6) from statement 2. solving them will give us the points at which it intersects x-axis.

let me know if i am right
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Re: coordinate geometry - DS [#permalink]  27 Jun 2010, 06:49

y crosses x axis, thus y=0.
Thus the equation becomes (x+a)(x+b) = 0
The roots are x = -a and x = - b

1 - a+b = -1 this is not sufficient.
2 - (0, -6), thus y crosses x axis at 6

I am not sure if the question is asking for the two points or only one point.
If only one point is requested, then answer 2 is sufficient.
If all points are needed, then answers 1 and 2 are sufficient.

Re: coordinate geometry - DS   [#permalink] 27 Jun 2010, 06:49
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