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twobagels
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 12 Apr 2021, 19:36
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B
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95% (hard)

Question Stats:

34% (02:10) correct 66% (02:18) wrong based on 195 sessions

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If h(x) = \(x^n\) * (\(x^2\)-4) + 21, for which of the following values of n does h have at least one real root?

A. 0
B. 1
C. 2
D. 4
E. There is no such value of n.
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B
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 14 Apr 2021, 08:45
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When n is odd, for higher -ve values of x, h(x) is definitely -ve and for higher +ve values of x, h(x) is definitely +ve. Since h(x) is a continuous function, it must cut x-axis at least once.

B


twobagels
If h(x) = \(x^n\) * (\(x^2\)-4) + 21, for which of the following values of n does h have at least one real root?

A. 0
B. 1
C. 2
D. 4
E. There is no such value of n.
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 18 Apr 2021, 23:37
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I do not follow the above solution! Bunuel Could you please assist!
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ShaikhMoice
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 22 May 2021, 01:01
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Experts please help with the solution.
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 22 May 2021, 01:36
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ShaikhMoice
Experts please help with the solution.
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ShaikhMoice

This question is not a GMAT like question so may skip it if you want.

Although, in case you are interested then you must read the theory of polynomial functions.

Ral root means the graph must cut X-axis at some point.

Since, Y coordinate on every point on X-axis is 0 therefore, substitute y = 0 and check that equation is consistent.

It happens here when n = 1, because then the equation is a cubic equation and there is a real value of x that we get for n=1

Real value = Any value which can be represented on Number line
Non-Real value = A value of teh type\(√-ve\)
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 19 Jul 2021, 22:51
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I will make it a simple example induced solution:
x^n * (x^2-4) + 21=0
=>(x^n)*x+4*x-4=-21
=>(x^n)*x+4*4-x=7*3*1
let us substitute x=3
=>3^n*7*1=3*7*1
when we substitute for thee powers of x
=>n=1
Hence IMO B
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If h(x)= x^n*(x^2 - 4) + 21, for which of the following values of n 15 Jan 2025, 06:09
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