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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
Joined: 06 Aug 2019
Posts: 111
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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09 Oct 2019, 04:17
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67% (01:35) correct 33% (01:49) wrong based on 54 sessions

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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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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
Economist GMAT Tutor Representative
Joined: 06 Aug 2019
Posts: 111
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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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 $$x+f=x+6\sqrt{3}.$$

$$x−2\sqrt{3}$$

$$x−6\sqrt{3}$$

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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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