GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 28 May 2020, 00:29

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Question about factorization of quadratic expression and roots

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
Joined: 22 Apr 2016
Posts: 16
Question about factorization of quadratic expression and roots  [#permalink]

Show Tags

New post 11 Jun 2016, 04:40
Hi,

If you have "ax²+bx+c=0" and if you can't find two numbers (c and d) whose sum is equal to "b" and whose product is equal to "c", does it mean that you can't factorize "ax²+bx+c" ?

And if you can't factorize "ax²+bx+c", does it mean that "ax²+bc+c=0" has no solution ?

Thanks a lot ! :) :)
Math Expert
avatar
V
Joined: 02 Aug 2009
Posts: 8601
Re: Question about factorization of quadratic expression and roots  [#permalink]

Show Tags

New post 11 Jun 2016, 04:59
jbyx78 wrote:
Hi,

If you have "ax²+bx+c=0" and if you can't find two numbers (c and d) whose sum is equal to "b" and whose product is equal to "c", does it mean that you can't factorize "ax²+bx+c" ?

And if you can't factorize "ax²+bx+c", does it mean that "ax²+bc+c=0" has no solution ?

Thanks a lot ! :) :)


Hi,

In normal scenario, a QUADRATIC equation will have two roots..
But it is possible these roots are imaginary number in some case...

Since GMAT does not deal with Imaginary number, there will be no solution for such equation as per GMAT..
_________________
Manhattan Prep Instructor
User avatar
G
Joined: 04 Dec 2015
Posts: 948
GMAT 1: 790 Q51 V49
GRE 1: Q170 V170
Re: Question about factorization of quadratic expression and roots  [#permalink]

Show Tags

New post 14 Jun 2016, 14:06
1
jbyx78 wrote:
Hi,

If you have "ax²+bx+c=0" and if you can't find two numbers (c and d) whose sum is equal to "b" and whose product is equal to "c", does it mean that you can't factorize "ax²+bx+c" ?

And if you can't factorize "ax²+bx+c", does it mean that "ax²+bc+c=0" has no solution ?

Thanks a lot ! :) :)


It depends on what you mean by 'not being able to find' those two numbers! Some quadratics include numbers that are incredibly tough to factor - for instance, x² + 2x - 399 = 0. I wouldn't want to be in the position of finding two numbers that multiply to -399, and add to 2. Nonetheless, those numbers exist - that quadratic factors to (x + 21)(x - 19) = 0. It would be easy to see a problem like that, and assume, after trying for a while, that those numbers didn't exist. Be careful about making that assumption.

If you see a quadratic that you're struggling to use this technique on, there's probably something else you could do. Try the quadratic formula. Or, try going back in the problem and seeing if you could simplify it differently. In the example I just gave, this is a much easier solution (the example, by the way, is actually adapted slightly from an Official Guide problem):

x² + 2x - 399 = 0
x² + 2x + 1 = 400
(x + 1)(x + 1) = 400
x + 1 = +/- 20
x = -21 or +19

chetan2u is right, too. There are some quadratics for which a solution just doesn't exist. And some quadratics only have one solution. You'll see the latter on the GMAT sometimes, but I'm not sure that I've ever seen the former.

Here's an example of a quadratic with no real solutions:

x² + x + 4 = 0

And here's an example of a quadratic with one solution:

x² + 4x + 4 = 0
_________________
Image

Chelsey Cooley | Manhattan Prep | Online tutoring and curriculum

My latest GMAT blog posts | My latest GRE blog posts | Suggestions for blog articles are always welcome!
Intern
Intern
avatar
Joined: 29 Sep 2014
Posts: 14
Re: Question about factorization of quadratic expression and roots  [#permalink]

Show Tags

New post 14 Jun 2016, 15:26
Good comments above, but also there is an easy way to check whether a quadratic equation has real roots using the quadratic formula.

\(x = (-b +/- \sqrt{b^2-4ac})/2a\)

If you take just the bit of the quadratic formula underneath the square root sign , you can use that to see if the equation has zero, one or two real roots.

If \(b^2-4ac\) is negative, then the equation has no real roots, if it is 0 then the equation has one root, and if it is positive then the equation has two real roots!
GMAT Club Bot
Re: Question about factorization of quadratic expression and roots   [#permalink] 14 Jun 2016, 15:26

Question about factorization of quadratic expression and roots

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne