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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
Posts: 6531
GMAT 1: 760 Q51 V42
GPA: 3.82
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
00:00

Difficulty:

75% (hard)

Question Stats:

48% (01:47) correct 52% (02:45) wrong based on 48 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) $$b^2-4ac>0$$

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" 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] ### Show Tags 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. No additional info. Insufficient. A. _________________ _________________________________________ Please Kudos, if you found this post helpful. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 6531 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and [#permalink] ### Show Tags 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 397 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. Answer: A _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$99 for 3 month Online Course"
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Re: In the x-y plane y=p(x)=ax^2+bx+c pass through (-1,0) and &nbs [#permalink] 15 Nov 2017, 00:49
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