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How many intersects with x-axis

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Intern
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Joined: 20 Aug 2010
Posts: 41
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Kudos [?]: 11 [0], given: 0

How many intersects with x-axis [#permalink] New post 26 Nov 2011, 11:54
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

100% (00:00) correct 0% (00:00) wrong based on 5 sessions
How many intersects with x-axis does y=x^2+2qx+r have

I) q^2>r

II) r^2>q
Intern
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Joined: 11 Nov 2011
Posts: 18
Followers: 0

Kudos [?]: 17 [0], given: 4

Re: How many intersects with x-axis [#permalink] New post 26 Nov 2011, 18:22
I think it is A.

The question can be rephrased: when is x^2+2qx+r = 0

Using the quadratic formula we find that x = (-2q +/- sqrt(4q^2 - 4r)/2)

From this we can see that there will be two solutions if 4q^2 - 4r > 0, one solution if 4q^2 - 4r = 0 and zero solutions if 4q^2 - 4r < 0.

From the information in 1.:
If q^2 > r then 4q^2 - 4r > 0.

SUFFICIENT - there are two points of intersection on the y axis.

From the information in 2.:
If r^2>q we don't know if 4q^2 - 4r is positive. We try two cases to demonstrate this:
if q = 1 and r = -2 then r^2>q and 4q^2 - 4r > 0
if q = 1 and r = 2 then r^2>q but 4q^2 - 4r < 0

This information is INSUFFICIENT.

So I chose A.
Re: How many intersects with x-axis   [#permalink] 26 Nov 2011, 18:22
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How many intersects with x-axis

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