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# Which of the following equations has a root in common with x^2−6x+8=0

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Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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18 Nov 2016, 03:55
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66% (01:43) correct 34% (01:35) wrong based on 228 sessions

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Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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18 Nov 2016, 04:37
Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

x^2-6x+8=0 can be factorized as (x-2) (x-4)

A. $$x^2+x−2=0$$ can be factorized as (x+2) (x-1)

B. $$x^2+4=0$$ can be factorized as x^2= -4 imaginary roots

C. $$x^2−12x+16=0$$ can be fctorized as x= (6+ 2(sqrt 5)), (6- 2(sqrt 5))

D. $$32−2x^2=0$$ can be factorized as x= 4, -4 shares a common root with x^2-6x+8=0

E. $$x^2−4x+16=0$$ can be factorized to get imaginary roots

Hence D
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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18 Nov 2016, 09:30
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Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

$$x^2−6x+8=0$$

Or, $$x^2−4x −2x +8=0$$

Or, $$x ( x − 4) −2 ( x − 4 ) = 0$$

So, x = 2 , 4

Check the options using x = 2 & 4..

Except (D) , none satisfies ..

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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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18 Nov 2016, 09:43
Top Contributor
Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

The solutions provided in the above posts are great, so I won't provide another solution that's similar.

However, I'd like to point out this this is one of those questions that require us to check/test each answer choice. That is, once we find the solutions to the given quadratic equation, we must then solve the equation in each answer choice until we find one that has a matching solution.
In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top.

For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... -questions

Cheers,
Brent
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 Nov 2016, 15:57
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Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

We can start by factoring the given equation of x^2 - 6x + 8 = 0:

(x - 4)(x - 2) = 0

x = 4 or x = 2

Now let’s analyze each answer choice to determine which has a root in common with x^2 - 6x + 8 = 0.

A) x^2 + x - 2 = 0

(x + 2)(x - 1) = 0

x = -2 or x = 1

Answer choice A DOES NOT have a root in common with x^2 - 6x + 8 = 0.

B) x^2 + 4 = 0

Since x^2 + 4 = 0 cannot be factored (over the real numbers), answer choice B DOES NOT have a root in common with x^2 - 6x + 8 = 0.

C) x^2 - 12x + 16 = 0

Since x^2 - 12x + 16 = 0 cannot be factored (over the integers), answer choice C DOES NOT have a root in common with x^2 - 6x + 8 = 0.

D) 32 - 2x^2 = 0

2(16 - x^2) = 0

2(4 + x)(4 - x) = 0

x = -4 or x = 4

Answer choice D DOES have a root in common with x^2 - 6x + 8 = 0.

E) x^2 - 4x + 16 = 0

Since x^2 - 4x + 16 = 0 cannot be factored (over the real numbers), answer choice E DOES NOT have a root in common with x^2 - 6x + 8 = 0.

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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 Jan 2017, 05:53
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 Jan 2017, 10:16
iliavko wrote:
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!

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Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 Jan 2017, 10:46
iliavko wrote:
Hi everyone!

Can please someone tell me where i can find how to solve these questions with quadratics quickly?

I start by doing the "what can be multiplied to give C and summed to give B" method. But it takes a lot of time!

What do I need to know of shortcuts here?

Thank you!

Bunuel has already provided the links the formula for solving any Quad Equation is as below -
Attachment:

qform01.gif [ 690 Bytes | Viewed 1879 times ]

Hope this helps...
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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30 Jan 2017, 08:57
1
You can plug in roots of equation x^2-6x+8=0 (which are 4 & 2 ) in a, b, c, d, e equations:
A. x^2+x−2=0
plug in 2→2^2+2-2≠0
plug in 4→4^2+4-2≠0

B. x^2+4=0
plug in 2→2^2+4≠0
plug in 4→4^2+4≠0

C. x^2−12x+16=0
plug in 2→2^2-12*2+16*2≠0
plug in 4→4^2-12*4+16≠0

D. 32−2x^2=0
plug in 2→32-2*2^2≠0
plug in 4→32-2*4^2=32-2*16=32-32=0 CHECK;4 IS ONE ROOT IN COMMUN!

E. x2−4x+16=0
plug in 2→2^2-4*2+16≠0
plug in 4→4^2-4*4+16≠0

hope this helps!
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 May 2017, 03:17
Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

Hi Bunuel,

I chose the correct answer but on the basis of most of the answer choice produce complex numbers as the root of the equation. However, I have seen here that people are considering only the real number as the root of the equations.

Does GMAT test complex numbers, or I am overthinking.

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Posts: 58323
Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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29 May 2017, 03:21
ravi11 wrote:
Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

Hi Bunuel,

I chose the correct answer but on the basis of most of the answer choice produce complex numbers as the root of the equation. However, I have seen here that people are considering only the real number as the root of the equations.

Does GMAT test complex numbers, or I am overthinking.

All numbers on the GMAT are by default real numbers.
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Re: Which of the following equations has a root in common with x^2−6x+8=0  [#permalink]

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07 Mar 2019, 20:54
Vinayak Shenoy wrote:
Bunuel wrote:
Which of the following equations has a root in common with $$x^2−6x+8=0$$?

A. $$x^2+x−2=0$$

B. $$x^2+4=0$$

C. $$x^2−12x+16=0$$

D. $$32−2x^2=0$$

E. $$x^2−4x+16=0$$

x^2-6x+8=0 can be factorized as (x-2) (x-4)

A. $$x^2+x−2=0$$ can be factorized as (x+2) (x-1)

B. $$x^2+4=0$$ can be factorized as x^2= -4 imaginary roots

C. $$x^2−12x+16=0$$ can be fctorized as x= (6+ 2(sqrt 5)), (6- 2(sqrt 5))

D. $$32−2x^2=0$$ can be factorized as x= 4, -4 shares a common root with x^2-6x+8=0

E. $$x^2−4x+16=0$$ can be factorized to get imaginary roots

Hence D

VINAYAK Shenoy

Could you please explain how to factorize C?

Kind regards!
Re: Which of the following equations has a root in common with x^2−6x+8=0   [#permalink] 07 Mar 2019, 20:54
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