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M03-18

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M03-18 [#permalink]

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New post 15 Sep 2014, 23:20
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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.


Answer: C
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Re: M03-18 [#permalink]

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New post 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.

Bunuel please clarify this.
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Re: M03-18 [#permalink]

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New post 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.


Answer: C


Bunel,

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

Thanks,
A
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Re: M03-18 [#permalink]

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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.


Answer: C


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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M03-18 [#permalink]

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New post 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.


Answer: C


can you please explain how you eliminated the square in the highlighted step. thanks
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Re: M03-18 [#permalink]

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New post 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.


Answer: C


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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M03-18 [#permalink]

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New post 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?
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New post 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.
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Re: M03-18 [#permalink]

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New post 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

Hence, Answer is C
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Re: M03-18 [#permalink]

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New post 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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New post 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M03-18   [#permalink] 09 Sep 2017, 03:30
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