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# M03-18

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Math Expert
Joined: 02 Sep 2009
Posts: 43894

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15 Sep 2014, 23:20
Expert's post
3
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00:00

Difficulty:

5% (low)

Question Stats:

69% (00:36) correct 31% (02:50) wrong based on 198 sessions

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How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
Posts: 43894

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15 Sep 2014, 23:20
Expert's post
1
This post was
BOOKMARKED
Official Solution:

How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

$$x^4 - 2x^2 +1=0$$;

$$(x^2-1)^2=0$$;

$$x^2-1=0$$;

$$(x-1)(x+1)=0$$. Either $$x=1$$ or $$x=-1$$. So, the given equation has two distinct roots.

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Joined: 06 Apr 2014
Posts: 4

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22 Nov 2014, 20:58
Value of x cant be negative as it equals to the even (4th) root of some expression.

So ,according to me x=1,therefore only one root.

Math Expert
Joined: 02 Sep 2009
Posts: 43894

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23 Nov 2014, 04:58
Expert's post
1
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gmattaker10 wrote:
Value of x cant be negative as it equals to the even (4th) root of some expression.

So ,according to me x=1,therefore only one root.

That's not correct. Plug -1 into the equation, does it hold true?
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Joined: 03 Aug 2015
Posts: 62
Concentration: Strategy, Technology
Schools: ISB '18, SPJ GMBA '17
GMAT 1: 680 Q48 V35

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03 Apr 2016, 07:27
Bunuel wrote:
Official Solution:

How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

$$x^4 - 2x^2 +1=0$$;

$$(x^2-1)^2=0$$;

$$x^2-1=0$$;

$$(x-1)(x+1)=0$$. Either $$x=1$$ or $$x=-1$$. So, the given equation has two distinct roots.

Bunel,

Could you pls explain the steps to get to the highlighted step?

Thanks,
A
Math Expert
Joined: 02 Sep 2009
Posts: 43894

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03 Apr 2016, 08:27
Expert's post
1
This post was
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ArunpriyanJ wrote:
Bunuel wrote:
Official Solution:

How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

$$x^4 - 2x^2 +1=0$$;

$$(x^2-1)^2=0$$;

$$x^2-1=0$$;

$$(x-1)(x+1)=0$$. Either $$x=1$$ or $$x=-1$$. So, the given equation has two distinct roots.

Bunel,

Could you pls explain the steps to get to the highlighted step?

Thanks,
A

It's a simple algebraic property: $$a^2-2ab+b^2=(a-b)^2$$
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Intern
Joined: 18 May 2016
Posts: 6

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12 Dec 2016, 18:45
Bunuel wrote:
Official Solution:

How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

$$x^4 - 2x^2 +1=0$$;

$$(x^2-1)^2=0$$;

[b]$$x^2-1=0$$;

$$(x-1)(x+1)=0$$. Either $$x=1$$ or $$x=-1$$. So, the given equation has two distinct roots.

can you please explain how you eliminated the square in the highlighted step. thanks
Math Expert
Joined: 02 Sep 2009
Posts: 43894

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13 Dec 2016, 00:56
bjklue wrote:
Bunuel wrote:
Official Solution:

How many distinct roots does the equation $$x^4 - 2x^2 + 1=0$$ have?

A. 0
B. 1
C. 2
D. 3
E. 4

$$x^4 - 2x^2 +1=0$$;

$$(x^2-1)^2=0$$;

[b]$$x^2-1=0$$;

$$(x-1)(x+1)=0$$. Either $$x=1$$ or $$x=-1$$. So, the given equation has two distinct roots.

can you please explain how you eliminated the square in the highlighted step. thanks

This is basics: number^2 = 0 --> number = 0.
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Joined: 23 Jan 2016
Posts: 225
Location: India
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01 Apr 2017, 07:54
Bunuel, though this may be a simple question, I always struggle to spot and close an open quadratic to a closed one, as has been done in this question. Is there any simple way to do so?
Math Expert
Joined: 02 Sep 2009
Posts: 43894

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02 Apr 2017, 04:12
OreoShake wrote:
Bunuel, though this may be a simple question, I always struggle to spot and close an open quadratic to a closed one, as has been done in this question. Is there any simple way to do so?

I guess the only way is through practice...
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Joined: 04 Apr 2017
Posts: 18

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19 Jun 2017, 20:53
In the given equation, substitute y = x^2.
The equation will reduce to a quadratic equation and the roots of y will 1.

Therefore, x^2 = 1 which means, x can be +1 or -1.
Verbal Forum Moderator
Joined: 19 Mar 2014
Posts: 992
Location: India
Concentration: Finance, Entrepreneurship
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19 Jun 2017, 21:26
Equation: x^4 - 2x^2 + 1=0

(x^2 - 1)^2 = 0

(x^2 - 1) = 0

x^2 = 1

Hence, x = +/- 1

So, this Equation will have two distinct roots

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Joined: 21 Mar 2017
Posts: 148
Location: India
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09 Sep 2017, 03:02
Bunuel,

I rejected -1 because (x2−1)2=0(x2−1)2=0.

Could you please provide few links to get a firm grip on such questions.

I have seen one solution before in which one value was eliminated because it was raised to the power of 4.
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Math Expert
Joined: 02 Sep 2009
Posts: 43894

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09 Sep 2017, 03:30
Prashant10692 wrote:
Bunuel,

I rejected -1 because (x2−1)2=0(x2−1)2=0.

Could you please provide few links to get a firm grip on such questions.

I have seen one solution before in which one value was eliminated because it was raised to the power of 4.

7. Algebra

For more check Ultimate GMAT Quantitative Megathread

Hope it helps.
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Re: M03-18   [#permalink] 09 Sep 2017, 03:30
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# M03-18

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