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# The graph of which of the following equations have two intersections w

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Manager
Joined: 30 May 2018
Posts: 88
GMAT 1: 620 Q42 V34
WE: Corporate Finance (Commercial Banking)
The graph of which of the following equations have two intersections w  [#permalink]

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21 Mar 2019, 07:42
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Difficulty:

65% (hard)

Question Stats:

54% (01:42) correct 46% (02:03) wrong based on 46 sessions

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The graph of which of the following equations have two intersections with axis-x?
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(C) y=-3x^2-5x+7
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1
GMAT Tutor
Joined: 24 Jun 2008
Posts: 1829
The graph of which of the following equations have two intersections w  [#permalink]

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21 Mar 2019, 08:37
2
The standard way (in high school algebra) to answer a question like this is by calculating something called the 'discriminant'. For any quadratic ax^2 + b^2 + c, the discriminant is equal to b^2 - 4ac. When the discriminant is positive, then the quadratic has two distinct roots, when it is zero, the quadratic has exactly one root, and when it is negative, the quadratic has no roots. Those roots will correspond to x-intercepts when you graph y = ax^2 + bx + c, so to answer this question, all you need to do is compute discriminants for each answer choice; only C gives a positive value.

But this really is not the kind of thing the GMAT tests, so you can safely ignore this question.
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Joined: 12 Feb 2015
Posts: 966
The graph of which of the following equations have two intersections w  [#permalink]

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Updated on: 21 Mar 2019, 08:55
MBA20 wrote:
The graph of which of the following equations have two intersections with axis-x?
(A) y=x^2+2x+3
(B) y=2x^2-3x+6
(C) y=-3x^2-5x+7
(D) y=2x^2-4x+2
(E) y=4x^2+2x+1

Only the equation mentioned in option C has two distinct roots as b^2-4ac > 0.

Hence option C is the correct answer.
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Originally posted by CAMANISHPARMAR on 21 Mar 2019, 08:52.
Last edited by CAMANISHPARMAR on 21 Mar 2019, 08:55, edited 1 time in total.
Intern
Joined: 18 May 2017
Posts: 12
Re: The graph of which of the following equations have two intersections w  [#permalink]

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21 Mar 2019, 08:54
using sridharayacharya's formula, A and B can be eliminate because the answers will be imaginary
D and E can be eliminated because the roots are of same magnitude
C is valid
Manager
Joined: 07 May 2018
Posts: 61
Re: The graph of which of the following equations have two intersections w  [#permalink]

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04 May 2019, 09:27
arimich wrote:
using sridharayacharya's formula, A and B can be eliminate because the answers will be imaginary
D and E can be eliminated because the roots are of same magnitude
C is valid

What is sridharayacharya's formula?
Re: The graph of which of the following equations have two intersections w   [#permalink] 04 May 2019, 09:27
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