is rx<0 (OG13)

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alex.gellatly: Master | Next Rank: 500 Posts; Posts: 435; Joined: Wed Nov 16, 2011 7:27 amFollowed by: 16 members; Thanked: 48 times

by alex.gellatly » Thu Aug 02, 2012 10:58 pm

If r and s are the roots of the equation x2+ bx + c = 0,where b and c are constants, is rs < 0 ?
(1) b<0
(2) c < 0

Thanks

A useful website I found that has every quant OG video explanation:

https://www.beatthegmat.com/useful-websi ... tml#475231

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Source: Beat The GMAT — Data Sufficiency | Thu Aug 02, 2012 10:58 pm

eagleeye: Legendary Member; Posts: 520; Joined: Sat Apr 28, 2012 9:12 pmFollowed by: 49 members; Thanked: 339 times; GMAT Score:770

by eagleeye » Fri Aug 03, 2012 3:17 am

alex.gellatly wrote:If r and s are the roots of the equation x2+ bx + c = 0,where b and c are constants, is rs < 0 ?
(1) b<0
(2) c < 0

Thanks

If r and s are roots (x-r)(x-s) = 0
=> x^2 -(r+s)x +rs = 0
=> x^2 -Sx + P = 0 (remember this for future)
Comparing with x^2+bx+c = 0, we see that
b = -(r+s)
c= rs

Hence the question rephrases as : is c<0?

Clearly, then, B is sufficient and correct

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Fri Aug 03, 2012 3:22 am

alex.gellatly wrote:If r and s are the roots of the equation x2+ bx + c = 0,where b and c are constants, is rs < 0 ?
(1) b<0
(2) c < 0

Thanks

For any question in the form axÂ²+bx+c=0:
The sum of the roots = -b/a.
The product of the roots = c/a.

In the equation above, a=1.
Thus, the product of the roots = c/1 = c.

Question rephrased: Is c<0?

Statement 1: b<0.
No way to determine whether c<0.
INSUFFICIENT.

Statement 2: c<0.
SUFFICIENT.

The correct answer is B.

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