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# If p and q are the roots of the quadratic equation ax^2+bx+c = 0,

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Director
Joined: 18 Feb 2019
Posts: 582
Location: India
GMAT 1: 460 Q42 V13
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If p and q are the roots of the quadratic equation ax^2+bx+c = 0,  [#permalink]

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29 Mar 2019, 00:19
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Difficulty:

55% (hard)

Question Stats:

60% (01:22) correct 40% (01:41) wrong based on 52 sessions

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If p and q are the roots of the quadratic equation ax^2+bx+c = 0, where a*b*c ≠ 0, is the product of p and q greater than 0?

I. |p + q| = |p| + |q|

II. ac > 0
NUS School Moderator
Joined: 18 Jul 2018
Posts: 1020
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
If p and q are the roots of the quadratic equation ax^2+bx+c = 0,  [#permalink]

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31 Mar 2019, 11:04
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3
$$ax^2+bx+c = 0.$$
Sum of the roots = p+q = -b/a
Product of roots = pq = c/a
Question, whether $$c/a > 0$$?

From S1:

|p+q| = |p| +|q|
Only possible when both p and q are either positive or negative.
In either of the cases c/a will be greater than 0.
Hence Sufficient.

From S2:

ac > 0.
Then either a and c are both positive or negative.
Hence Sufficient.

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Intern
Joined: 26 Aug 2018
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Re: If p and q are the roots of the quadratic equation ax^2+bx+c = 0,  [#permalink]

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01 Apr 2019, 10:03

Posted from my mobile device
NUS School Moderator
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Posts: 1020
Location: India
Concentration: Finance, Marketing
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Re: If p and q are the roots of the quadratic equation ax^2+bx+c = 0,  [#permalink]

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01 Apr 2019, 10:20
Tulsi123 wrote:

Posted from my mobile device

Hey Tulsi123, Which part of my explanation is not clear?
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Re: If p and q are the roots of the quadratic equation ax^2+bx+c = 0,   [#permalink] 01 Apr 2019, 10:20
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