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

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Senior Manager
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Joined: 18 Feb 2019
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GMAT 1: 490 Q47 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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New post 29 Mar 2019, 00:19
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A
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D
E

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
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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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New post 31 Mar 2019, 11:04
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\(ax^2+bx+c = 0.\)
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.

D is the answer.
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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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New post 01 Apr 2019, 10:03
Please elaborate the explanation

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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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New post 01 Apr 2019, 10:20
Tulsi123 wrote:
Please elaborate the explanation

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

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