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If (x - 2 3^1/2) is one of the quadratic X^2 + (4 3^1/2)x - 36, what

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Economist GMAT Tutor Representative
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If (x - 2 3^1/2) is one of the quadratic X^2 + (4 3^1/2)x - 36, what  [#permalink]

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New post 09 Oct 2019, 04:17
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If \((x - 2 \sqrt{3})\) is one of the quadratic \(x^2 + (4 \sqrt{3})x - 36,\) what is the other factor?

A. \(x + 2 \sqrt{3}\)

B. \(x + 4 \sqrt{3}\)

C. \(x + 6 \sqrt{3}\)

D. \(x - 2 \sqrt{3}\)

E. \(x - 6 \sqrt{3}\)

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Re: If (x - 2 3^1/2) is one of the quadratic X^2 + (4 3^1/2)x - 36, what  [#permalink]

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New post 11 Oct 2019, 22:35
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TheEconomistGMAT wrote:
If \((x - 2 \sqrt{3})\) is one of the quadratic \(x^2 + (4 \sqrt{3})x - 36,\) what is the other factor?

A. \(x + 2 \sqrt{3}\)

B. \(x + 4 \sqrt{3}\)

C. \(x + 6 \sqrt{3}\)

D. \(x - 2 \sqrt{3}\)

E. \(x - 6 \sqrt{3}\)


Formula: For the quadratic equation ax^2 + bx + c = 0,
Sum of the roots = -b/a & Product of the roots = c/a


For the given quadratic, a = 1, b = 4\(\sqrt{3}\), c = -36

One of the root/factor = \(2 \sqrt{3}\)
Let the other root be r
--> Product of the roots = c/a
--> \(2 \sqrt{3}\)*r = -36/1
--> \(r = -36/2\sqrt{3}\) = \(-6\sqrt{3}\)

So, the other root is \(x + 6 \sqrt{3}\)

IMO Option C
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Re: If (x - 2 3^1/2) is one of the quadratic X^2 + (4 3^1/2)x - 36, what  [#permalink]

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New post 13 Oct 2019, 00:38

Official Explanation



The issue is factoring a quadratic. Remember, a quadratic of the form \(x^2+bx+c\) can be factored into \((x+e)(x+f)\) where \(e+f=b\) and \(ef=c\)
In this case, it is easiest to use the fact that \(e+f=b\)a since you are given one of the factors and b.

Since \((x−2\sqrt{3})\) is a factor, you know that \(e=−2\sqrt{3}\). (Of course, it could be the case that \(f=−2\sqrt{3}\), but \(e\) and \(f\) are interchangeable, so it doesn't matter which one you assign to the known value.)

In the given quadratic, you can see that b, the coefficient of the x-term, is \(4\sqrt{3}\). That gives you the equation:

\(e+f=b\)

\(−2\sqrt{3}+f=4\sqrt{3}.\)

Adding \(2\sqrt{3}\) to both sides gives

\(f=6\sqrt{3.}\)

Thus, the other factor is \(x+f=x+6\sqrt{3}.\)

\(x−2\sqrt{3}\)

\(x−6\sqrt{3}\)

Answer: C
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Re: If (x - 2 3^1/2) is one of the quadratic X^2 + (4 3^1/2)x - 36, what   [#permalink] 13 Oct 2019, 00:38
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