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root comparison

by shikh » Fri Dec 02, 2011 5:07 am
A: x2 + 6x - 40 = 0
B: x2 + kx + j = 0
Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?
1.j = k
2.k is negative
OA:B
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by kanwar86 » Fri Dec 02, 2011 5:16 am
shikh wrote:A: x2 + 6x - 40 = 0
B: x2 + kx + j = 0
Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?
1.j = k
2.k is negative
OA:B
correct answer is B)
Regards

Kanwar

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by GMATGuruNY » Fri Dec 02, 2011 7:12 am
shikh wrote:A: x2 + 6x - 40 = 0
B: x2 + kx + j = 0
Which is larger, the sum of the roots of equation A or the sum of the roots of equation B?
1.j = k
2.k is negative
OA:B
Given ax² + bx + c = 0, the SUM of the roots = -b/a.

Thus:
In A, the sum of the roots = -6/1 = -6.
In B, the sum of the roots = -k/1 = -k.

Statement 1: j=k
No way to determine the sum of the roots of equation B.
INSUFFICIENT.

Statement 2: k is negative
Thus, the sum of the roots of equation B must be POSITIVE.
Since the sum of the roots of equation A is negative, the sum of the roots of equation B is greater.
SUFFICIENT.

The correct answer is B.

Also helpful:
Given ax² + bx + c = 0, the PRODUCT of the roots = c/a.
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