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# In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and [#permalink]

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13 Nov 2017, 00:11
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Difficulty:

75% (hard)

Question Stats:

47% (00:38) correct 53% (01:58) wrong based on 34 sessions

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[GMAT math practice question]

In the x-y plane $$y=p(x)=ax^2+bx+c$$ pass through (-1,0) and (1,0). Is $$p(0)<0$$?

1) $$a>0$$
2) $$b^2-4ac>0$$
[Reveal] Spoiler: OA

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Intern
Joined: 28 Dec 2010
Posts: 49
Re: In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and [#permalink]

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13 Nov 2017, 02:44
This is a parabola. Since it already has 2 roots, we need to find whether it is facing upwards or downwards.

1. It is facing upwards.
p(0) <0
Sufficient.

2. We already know this since it has 2 roots. It would be helpful to know if we didn't new those 2 points.
Insufficient.

A.
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Math Revolution GMAT Instructor
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Re: In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and [#permalink]

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15 Nov 2017, 00:49
=>

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember that equal number of variables and independent equations ensures a solution

p(-1) = a – b + c = 0
p(1) = a + b + c = 0
Since we have 3 variables, a, b and c and 2 equations, D is most like to be the answer.

Condition 1)

Attachment:

11.13.png [ 7.33 KiB | Viewed 187 times ]

Since the leading coefficient a is positive, the parabola is concave up and p(0) < 0.
This is sufficient.

Condition 2)
It means the graph intersects x-axis twice and that the discriminant is positive.
We have two cases that the parabola could be concave up or concave down.

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both con 1) and con 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. D is most likely to be the answer using con 1) and con 2) separately according to DS definition. Obviously, there may be cases where the answer is A, B, C or E.

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Re: In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and   [#permalink] 15 Nov 2017, 00:49
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