If f(x) = x^n - a = 0, how many REAL roots does x have?
(1) a < 0
(2) n = 2k, where k is a positive integer
(1) a < 0
(2) n = 2k, where k is a positive integer
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Rooted to roots
Source: Beat The GMAT — Data Sufficiency |
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shashank.ism
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x^n - a = 0 --> x= a^(1/n)austin wrote:If f(x) = x^n - a = 0, how many REAL roots does x have?
(1) a < 0
(2) n = 2k, where k is a positive integer
so there can be many solution depending on a and n
St. 1: a<0 i.e. -ve values then also many soln. --------------not sufficient
St. 2: n=2k then also many soln. --------------not sufficient
combined : since a is -ve and and we are taking nth root where n is even (as n=2k)
so there will be no solution
Hence, it is sufficient Ans C
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1) a<0austin wrote:If f(x) = x^n - a = 0, how many REAL roots does x have?
(1) a < 0
(2) n = 2k, where k is a positive integer
is not sufficient
Say when n = 1 and a= -3
x+3 has one root x = -3
when n =2 and a= -3
x^2+3 = 0 doesn't have real roots
2) n = 2k is not sufficient
say k = 1 and a = 1
it has 2 roots
x^2-1 =0 has 2 roots
say k = 1 and a = -1
x^2+1=0 has 0 roots
Combining
x^2k + (a positive number) =0 doesnt have any real roots
So, C
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Ian Stewart
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There's an issue with the wording here. When the question uses the word 'roots', what it means is 'solutions to the equation'. It makes no sense to talk about how many 'roots' x has in that case; they mean to ask how many roots 'x^n - a = 0' has, or as is sometimes said, how many roots f(x) has. If you simply talk about the 'roots' of a number or letter, it would be natural to take that to mean square roots, cube roots, and so on, which is not at all what the question is talking about. If the wording in the post above is that used in the source, then there are problems with that source.austin wrote:If f(x) = x^n - a = 0, how many REAL roots does x have?
(1) a < 0
(2) n = 2k, where k is a positive integer
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shashank.ism
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ian that was a nice explanation related to roots..will keep it in mind.Ian Stewart wrote:There's an issue with the wording here. When the question uses the word 'roots', what it means is 'solutions to the equation'. It makes no sense to talk about how many 'roots' x has in that case; they mean to ask how many roots 'x^n - a = 0' has, or as is sometimes said, how many roots f(x) has. If you simply talk about the 'roots' of a number or letter, it would be natural to take that to mean square roots, cube roots, and so on, which is not at all what the question is talking about. If the wording in the post above is that used in the source, then there are problems with that source.austin wrote:If f(x) = x^n - a = 0, how many REAL roots does x have?
(1) a < 0
(2) n = 2k, where k is a positive integer
My Websites:
www.mba.webmaggu.com - India's social Network for MBA Aspirants
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IMO A
b'cos ques ans how many real roots r thr..
so option A says that NO SOLUTION.... so that mean we get ans A
ta
b'cos ques ans how many real roots r thr..
so option A says that NO SOLUTION.... so that mean we get ans A
ta
