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If x^5 + x^2 < 0, then which one of the following must be true?

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If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 02 Apr 2019, 04:01
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

66% (01:02) correct 34% (01:18) wrong based on 29 sessions

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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 02 Apr 2019, 04:09
Bunuel wrote:
If \(x^5 + x^2 < 0\), then which one of the following must be true?

(A) \(x < –1\)

(B) \(x < 0\)

(C) \(x > 0\)

(D) \(x > 1\)

(E) \(x^4 < x^2\)



Given,

\(x^5 + x^2 < 0\)

\(x^2 \geq 0\)

\(x^5\)must be negative.

So, x is negative. but we don't know whether x is fraction or integer.

x must be integer. Fraction doesn't wok here.

A is the best answer.
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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 02 Apr 2019, 05:02
\(x^5\)+\(x^2\)<0
\(x^2\)*(\(x^3\)+1)<0
As \(x^2\) cant be negative, so (\(x^3\)+1) is negative and x<-1

IMO
Ans: A
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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 02 Apr 2019, 06:05
IMO A


C and D both give positive values

E will not hold true for negative fraction say -1/2

for B , put x=-1 and it make expression = 0 , again out of scope


So IMP A .


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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 03 Apr 2019, 03:50
Bunuel wrote:
If \(x^5 + x^2 < 0\), then which one of the following must be true?

(A) \(x < –1\)

(B) \(x < 0\)

(C) \(x > 0\)

(D) \(x > 1\)

(E) \(x^4 < x^2\)


x^5+x^2<0
shall stand valid only when x is -ve and <-1
IMO A
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Re: If x^5 + x^2 < 0, then which one of the following must be true?  [#permalink]

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New post 07 Apr 2019, 18:24
Bunuel wrote:
If \(x^5 + x^2 < 0\), then which one of the following must be true?

(A) \(x < –1\)

(B) \(x < 0\)

(C) \(x > 0\)

(D) \(x > 1\)

(E) \(x^4 < x^2\)


Let’s simplify the inequality:

x^5 + x^2 < 0

x^2(x^3 + 1) < 0

Divide both sides by x^2 (notice that x can’t be 0, so x^2 is positive):

x^3 + 1 < 0

x^3 < -1

x < ^3√(-1)

x < -1

Answer: A
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Re: If x^5 + x^2 < 0, then which one of the following must be true?   [#permalink] 07 Apr 2019, 18:24
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