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# In an X Y Plane, how many points are common to the X axis

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Senior Manager
Joined: 21 Aug 2003
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Location: Bangalore
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In an X Y Plane, how many points are common to the X axis [#permalink]  15 Nov 2003, 23:23
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"In an X Y Plane, how many points are common to the X axis and the curve defined by y = ax2 + bx + c ?"
1. b < 0.
2. c < 0.

Basicaly, question is asking how many roots the quadratic equation: y = ax2 + bx + c can have.
Now this depends on determinant of the equation: b^2 - 4*a*c
If above is zero, than we have equal roots and curve y will touch X axis at only one point, Else it may touch two points or none at all.

any ideas...?
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
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Kudos [?]: 2 [0], given: 0

I think the answer should be E as well.

Of course the information that Statement (1) gives us doesn't help, but it would have helped to know something about a along with c.
Director
Joined: 13 Nov 2003
Posts: 971
Location: Florida
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Kudos [?]: 35 [0], given: 0

as B states C<0, thus on X-axis i.e. X=0, C is the only value that can provide you the result.
I vote for B. BTW expalnation is not sufficient..i know ...
Intern
Joined: 27 Jul 2003
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to find the points on x axis, u have to put y=0 and not x=0

if c is negative, b^2 - 4ac will be positive and hence there will be two real roots.

Hence statement 2 alone is enough to solve the problem where as statement 1 alone is not.

Bharathi.
GMAT Instructor
Joined: 07 Jul 2003
Posts: 770
Location: New York NY 10024
Schools: Haas, MFE; Anderson, MBA; USC, MSEE
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Kudos [?]: 70 [0], given: 0

bhars18 wrote:
to find the points on x axis, u have to put y=0 and not x=0

if c is negative, b^2 - 4ac will be positive and hence there will be two real roots.

Hence statement 2 alone is enough to solve the problem where as statement 1 alone is not.

Bharathi.

Hmm. What if a was a large negative number and 4ac > b^2?
_________________

Best,

AkamaiBrah
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

CEO
Joined: 15 Aug 2003
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Kudos [?]: 718 [0], given: 781

vicks, did you get a solution to this.

thanks
praetorian
Intern
Joined: 27 Jul 2003
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Quote:
Hmm. What if a was a large negative number and 4ac > b^2?

Oops... that would make it E

Bharathi.
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