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Intern
Joined: 17 Jul 2013
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04 Sep 2013, 10:49
Hi friends,

I´m had been problems to solve by factoring the next equation. (x^2)- 13x-130=0
Is there anyone who can help me to solve it?

Magoosh GMAT Instructor
Joined: 28 Dec 2011
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04 Sep 2013, 14:37
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bandala wrote:
Hi friends,

I´m had been problems to solve by factoring the next equation. (x^2)- 13x-130=0
Is there anyone who can help me to solve it?

Dear bandala,

First of all, here's a general article on the topic.
http://magoosh.com/gmat/2012/algebra-on ... to-factor/

For this question, we need two numbers
(a) whose product is -130, so one is positive and one is negative
and
(b) whose sum is -13 (so the one with the larger absolute value is negative)

130 = 13*10, but those two numbers are too close
130 = 5*26
130 = 2*65
Those are the only whole number factors that multiply to 130, and none of them work.

The problem is --- this quadratic is 100% unfactorable. The solutions involve expressions with the square-root of 689, which is an unsimplifiable square-root. The GMAT would NEVER ask you to factor such an equation. If this equation appeared in some form on the GMAT, it would have to be a question that could be solved without factoring it. The GMAT would not expect you to find the solutions without a calculator.

Does this make sense?
Mike
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Mike McGarry
Magoosh Test Prep

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05 Sep 2013, 11:39
Yes, you right, following the rules mentioned to get the second and the third number is imposible by factoring. Thanks a lot for the clue " GMAT would NEVER ask you to factor such an equation"

Thanks again!
Veritas Prep GMAT Instructor
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05 Sep 2013, 21:19
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Yup some quadratic expressions won't have simple "real number" solutions. The great thing about having no calculator on the GMAT is that the numbers they give will always be solvable fairly quickly by inspection, that is determining what the factors are of C and combining them (+ or -) to form B.

This question reminds me of a question we had in university. What are the roots of $$x^2 + 2x +10$$. There's no way to solve this without complex roots, as you can pretty quickly see that no integers (or fractions) will work here. Thankfully, this also means it would never be on the GMAT.

Remember the next time the GMAT frustrates you: everything you can be asked on the exam is known and the math never gets that bad. I know the exam isn't always straight forward but at least it's fair.

Hope this helps!
-Ron
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