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Which of the following equations has a root in common with x^2−7x+12=0

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Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 07 Mar 2016, 07:52
2
2
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A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (01:25) correct 15% (01:55) wrong based on 136 sessions

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Re: Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 07 Mar 2016, 19:12
roots for x^2 - 7x+12 = 0 are 4 and 3

only equation
x^2 - x - 12 = 0 has a same similar root

Ans: B
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Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 15 Jun 2016, 02:20
1
factorize \(x^2\)-\(7x\)+\(12\) we get (\(x-3\))(\(x-4\))
So roots of the equation are 3 and 4
substitute both these values to see which option gives 0 as answer
(Note - only 1 of the roots will satisfy the equation)

in option B \(x^2\)-\(x\)-\(12\) if we substitute x= 4 we get the answer as 0
Correct Answer - B
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Re: Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 15 Jun 2016, 04:01
Bunuel wrote:
Which of the following equations has a root in common with x^2−7x+12=0 ?

A. x^2+1=0
B. x^2−x−12=0
C. x^2−8x−4=0
D. 3x^2−9=0
E. x^2+x-6=0


If we carefully look at the given equation we can arrange it in the following manner:
(x-3)(x-4) = 0
so the two roots are 3 and 4.

Now put 3 and 4 in given equations. The equation in which one of them gives value 0, that will be our answer.

(A) putting 3: we get 10; Putting 4 we get 17. Reject this option [by the way x^2+1 cannot have real roots]
(B) putting 3: we get 6; Putting 4 we get 0. This is the equation.

We are lucky . no need to check other options.

B is the answer.
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Re: Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 16 Oct 2017, 21:03
Bunuel wrote:
Which of the following equations has a root in common with x^2−7x+12=0 ?

A. x^2+1=0
B. x^2−x−12=0
C. x^2−8x−4=0
D. 3x^2−9=0
E. x^2+x-6=0


B is the correct answer

I believe the trick here is not solving the equation and it's roots but how to find the correct answer in the shortest time possible. I didn't substitute any numbers, I just looked at the answer choices and noticed that B can be solved by the same numbers (4&3) but with a different sign for (3).

I believe substitution for all the answer choices would be a waste of time, esp. that you have 2 numbers to substitute with (4&3)
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Re: Which of the following equations has a root in common with x^2−7x+12=0  [#permalink]

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New post 19 Oct 2017, 09:23
Bunuel wrote:
Which of the following equations has a root in common with x^2−7x+12=0 ?

A. x^2+1=0
B. x^2−x−12=0
C. x^2−8x−4=0
D. 3x^2−9=0
E. x^2+x-6=0


If two quadratic equations have a common root, then they have a common factor. Thus, we need to factor the left-hand side of the equation. Breaking down the given quadratic equation, we have:

(x - 4)(x - 3) = 0

We need to find an answer choice with at least one identical factor.

Looking at answer choice B we have:

x^2 − x − 12 = 0

(x - 4)(x + 3) = 0

Since answer choice B shares the factor (x - 4), both equations will have a common root, which is 4.

Answer: B
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Re: Which of the following equations has a root in common with x^2−7x+12=0 &nbs [#permalink] 19 Oct 2017, 09:23
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