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

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Senior Manager
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In an X Y Plane, how many points are common to the X axis [#permalink] New post 15 Nov 2003, 23:23
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A
B
C
D
E

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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.

i think answer should be E. but official answer is B.
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...?
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 [#permalink] New post 16 Nov 2003, 06:27
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.
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 [#permalink] New post 16 Nov 2003, 12:51
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 ... :no
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 [#permalink] New post 17 Nov 2003, 22:53
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.
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 [#permalink] New post 18 Nov 2003, 01:27
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?
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 [#permalink] New post 23 Nov 2003, 20:05
vicks, did you get a solution to this.

thanks
praetorian
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 [#permalink] New post 27 Nov 2003, 07:03
Quote:
Hmm. What if a was a large negative number and 4ac > b^2?


Oops... that would make it E 8-)

Bharathi.
  [#permalink] 27 Nov 2003, 07:03
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