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# Q. At how many points does the line y = ax^2 + 2qx + r cut

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Manager
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Q. At how many points does the line y = ax^2 + 2qx + r cut [#permalink]  18 Aug 2003, 04:55
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Q. At how many points does the line y = ax^2 + 2qx + r cut the X-axis.

1) q> r^2

2) 2r > q^2

I do not have the official answer, but hope you can solve this
Manager
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[#permalink]  18 Aug 2003, 06:22
are you sure that everything is correct in the statement?

component ax^2 indicates that this is not a line, it's a parabola.
what is the source of question?

anyway, the Line always crosses and axis in one point
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Manager
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Re: HARD DS [#permalink]  18 Aug 2003, 06:44
MBA04 wrote:
Q. At how many points does the line y = ax^2 + 2qx + r cut the X-axis.

1) q> r^2

2) 2r > q^2

I do not have the official answer, but hope you can solve this

For any quadratic ax^2+bx+c,

if b^2-4ac >0, then the equation has two real roots (i.e. it cuts the x axis in two distinct points)

if b^2-4ac = 0, then the equation has two real roots that are equal (i.e. it cuts in one distinct point)

if b^2-4ac < 0 then the equation does not have any real roots

Now condition (1) tells us that q>r^2. But this does not tell us whether 4q^2-4ar is >0, =0 or <0 since the value of a in unknown

Condition (2) tells us that 2r>q^2. Again, the value of a is unknown so we cannot arrive at a clear answer to the question.

Together also they do not help.

Hence E
Manager
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[#permalink]  18 Aug 2003, 07:52
As I told you, I don┬┤t have the offical answer, but i agree with the answer and explanation of prashant

any other?
[#permalink] 18 Aug 2003, 07:52
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# Q. At how many points does the line y = ax^2 + 2qx + r cut

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