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Which if the following has a root in common with x^2 - 6x + 5 = 0

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Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 22 May 2018, 17:25
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A
B
C
D
E

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  35% (medium)

Question Stats:

69% (01:31) correct 31% (01:57) wrong based on 101 sessions

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Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0
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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 22 May 2018, 18:35
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1
Option D

\(x^2-6x+5\) = \((x-5)\)\((x-1)\)

roots = 5 or 1

- now check/test each answer choice using x = 1 and x = 5 (In these situations, always check the answer choices from E to A: https://www.gmatprepnow.com/articles/handling-%E2%80%9Canalyze-answer-choices%E2%80%9D-questions)

Only D satisfies.
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Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 23 May 2018, 07:05
2
Abhimanyu111 wrote:
Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0

Factor the quadratic to find its roots
\(x^2 - 6x + 5 = 0\)
\((x - 1)(x - 5)= 0\)
\(x = 1\) or \(x = 5\)

Plug both roots into the answer choices. Scan the choices first.

Eliminate A (inevitable positive result, not 0); and
Eliminate C (with roots this small, inevitable negative result).*

FillFM 's link** and GMATPrepNow 's article are helpful. +1

The arithmetic here is easy. I started with B. This question took a little over half a minute.
Analysis of all choices for those who are curious:

A. \(x^2+ 1 = 0\)
\(x=1\): \((1+1) = 2\) NO
\(x=5\): \((25+1)=26\) NO

B. \(x^2 - x-2 = 0\)
\(x=1\): \((1-1-2) = -2\) NO
\(x=5\): \((25-5-2) = 18\) NO

C. \(x^2 - 10x - 5 = 0\)
\(x=1\): \((1-10-5) = -14\)
\(x=5\): \((25-50-5) = -30\)

D. \(2x^2 - 2 = 0\)
\(x=1\): \((2-2) = 0\) YES
Finished. We just need one root.

In case there is doubt, (D) cont.:
\(x=5\): \((50-2=48)\) NO. Does not matter. We need "a" root (one) in common. We have \(x = 1\)

E. \(x^2 - 2x-3 = 0\)
\(x=1\): \((1-2-3) = -4\)
\(x=5\): \((25-10-3) = 12\) NO

ANSWER D

*Eliminate A: Both roots are positive. Answer A has two positive terms and a plus sign. Positive roots cannot make that equation true.
Eliminate C: For roots 1 and 5, the squared \(a\) term is not great enough to overcome the negative coefficient of the \(b\) term
** FillFM links to an excellent article that recommends starting with E for "analyze the answer choices". (The stats are startling.) I'm a bit paranoid. GMAC adapts to public warnings.

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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 20 Jun 2018, 08:11
x^2 - 6x + 5 = 0
Has two roots
(x-1)(x-5)=0
X=1,5

And 1 is root of choice D
i.e. 2(x^2-1)=0
2(x+1)(x-1)=0
X=1,-1

Hence D is answer

Give kudos if it helps

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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 20 Jun 2018, 08:24
Option D has the root x = 1 common with the equation given in stimulus.
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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0  [#permalink]

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New post 21 Jun 2018, 15:56
Abhimanyu111 wrote:
Which if the following has a root in common with x^2 - 6x + 5 = 0

A. x^2+ 1 = 0

B. x^2 - x-2 = 0

C. x^2 - 10x - 5 = 0

D. 2x^2 - 2 = 0

E. x^2 - 2x-3 = 0


Simplifying the given equation, we have:

x^2 - 6x + 5 = 0

(x - 5)(x - 1) = 0

x = 5 or x = 1

By scanning through the answer choices, we see x = 1 is a solution to 2x^2 - 2 = 0. Thus, choice D is the answer.

Answer: D.
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Re: Which if the following has a root in common with x^2 - 6x + 5 = 0   [#permalink] 21 Jun 2018, 15:56

Which if the following has a root in common with x^2 - 6x + 5 = 0

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