It is currently 23 Sep 2017, 14:37

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# How to solve quadratics when a does NOT equal 1

Author Message
TAGS:

### Hide Tags

Intern
Joined: 11 Jul 2014
Posts: 26

Kudos [?]: 7 [0], given: 6

Location: United Kingdom

### Show Tags

27 Jul 2014, 11:23
1
This post was
BOOKMARKED
For example here: running-at-their-respective-constant-rates-machine-x-takes-98599.html
I don't really get how can one quickly factor $$5t^2-34t+24=0$$
If a=1 it is easy a1*a2=c, a1+a2=-b, but what if a=/=1?

Thanks!

Kudos [?]: 7 [0], given: 6

Intern
Joined: 22 Jun 2013
Posts: 46

Kudos [?]: 9 [0], given: 1

Concentration: Healthcare
Schools: Johnson '17 (S)
GMAT Date: 04-24-2014
GPA: 3.67
WE: Consulting (Health Care)

### Show Tags

27 Jul 2014, 12:41
imoi wrote:
For example here: running-at-their-respective-constant-rates-machine-x-takes-98599.html
I don't really get how can one quickly factor $$5t^2-34t+24=0$$
If a=1 it is easy a1*a2=c, a1+a2=-b, but what if a=/=1?

Thanks!

Hey dude,

When I do quadratics, I always focus on the "c" portion, in this case the 24. This is helpful because you do not have to even consider the "a", or in this case the 5. Start with the factor pairs for 24 (12,2) (3,8) (4,6). Now think about which, of these three pairs, produces a -34 if you multiply one term by 5 and add it to the other? Also because 24 is (+), both factors need to be either positive or negative. In this case, both will be negative because of -34.

Start with (12,2): hmmm... [-12*5] + -2? No that doesn't give us -34. What about -12 + [-2*5]? No that doesn't give us -34 either
What about (4,6)? Oh look, -4+[-6*5] gives us -34! Therefore -4 and -6 must be our factor pair

(5t-4)(t-6)
_________________

MGMAT1 - 650 (Q44, V35)
MGMAT2 - 670 (Q42, V39)
MGMAT3 - 640 (Q44, V34)
MGMAT4 - 630 (Q41, V35)
GMATPrep1 - 720 (Q48, V40)
GMATPrep2 - 720 (Q48, V41)
MGMAT5 - 690 (Q45, V39)
GMATPrep3 - 700 (Q47, V39)
GMATPrep4 - 710 (Q49, V38)

Test Day: 740 (Q49, V41)

Kudos [?]: 9 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124650 [0], given: 12079

Re: How to solve quadratics when a does NOT equal 1 [#permalink]

### Show Tags

27 Jul 2014, 14:24
imoi wrote:
For example here: running-at-their-respective-constant-rates-machine-x-takes-98599.html
I don't really get how can one quickly factor $$5t^2-34t+24=0$$
If a=1 it is easy a1*a2=c, a1+a2=-b, but what if a=/=1?

Thanks!

Theory on Algebra: algebra-101576.html
Algebra - Tips and hints: algebra-tips-and-hints-175003.html

DS Algebra Questions to practice: search.php?search_id=tag&tag_id=29
PS Algebra Questions to practice: search.php?search_id=tag&tag_id=50

Special algebra set: new-algebra-set-149349.html

Hope this helps.
_________________

Kudos [?]: 124650 [0], given: 12079

Manager
Joined: 11 Jun 2014
Posts: 57

Kudos [?]: 34 [0], given: 3

Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)

### Show Tags

03 Aug 2014, 19:44
I think the speed with factorization comes with practice.. you have to be using numbers, especially multiplication tables so often that they pop into your mind. I don't think there can be a 'method' to do it 'quickly'

for 5(t^2)-34t+24 .. I just multiply a*c --> 5*24 = 120.

now of course you could try to factorize 120 and list all its factors.. thats the 'method'. But the moment I see 120 and -34, I know the second term should be split into -30 and -4 ( 30 * 4 =120 pops into my mind immediately)

5(t^2) -30t -4t +24 = 5t( t-6) -4(t-6) = (t-6) (5t-4)..

Of course this gets more difficult when dealing with bigger numbers or multiplications we use less often...

Kudos [?]: 34 [0], given: 3

Director
Affiliations: GMATQuantum
Joined: 19 Apr 2009
Posts: 603

Kudos [?]: 481 [0], given: 17

Re: How to solve quadratics when a does NOT equal 1 [#permalink]

### Show Tags

15 Aug 2014, 12:06
I would recommend using the method that @sshrivats described above. Generally, on the GMAT the quadratics that have a coefficient other than 1 can be solved by reasonably guessing the factors. They will not give you a quadratic that is a pain to factor.

Another example of such a quadratic from an official GMAT equation is: 2x^2 - 5x - 33 = 0, here the product of 2 and (-33) is -66, the two numbers that give the product of 66 are 11 and 6(they also give a add up to 5 if we choose the right signs), we have to choose the signs based on the two numbers adding up to -5(the coefficient of x). In this case the two numbers are -11 and 6. The quadratic equation then becomes:

2x^2 - 11x + 6x - 33 = 0

x(2x-11) + 3(2x-11)=0

(x+3)(2x-11)=0

Cheers,
Dabral

Kudos [?]: 481 [0], given: 17

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1854

Kudos [?]: 2525 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: How to solve quadratics when a does NOT equal 1 [#permalink]

### Show Tags

10 Sep 2014, 19:37
imoi wrote:
For example here: running-at-their-respective-constant-rates-machine-x-takes-98599.html
I don't really get how can one quickly factor $$5t^2-34t+24=0$$
If a=1 it is easy a1*a2=c, a1+a2=-b, but what if a=/=1?

Thanks!

You may use the formula:

$$ax^2 + bx + c = 0$$

$$Roots = \frac{-b + - \sqrt{b^2 - 4ac}}{2a}$$
_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2525 [0], given: 193

Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7615

Kudos [?]: 16942 [0], given: 230

Location: Pune, India
Re: How to solve quadratics when a does NOT equal 1 [#permalink]

### Show Tags

10 Sep 2014, 23:19
imoi wrote:
For example here: running-at-their-respective-constant-rates-machine-x-takes-98599.html
I don't really get how can one quickly factor $$5t^2-34t+24=0$$
If a=1 it is easy a1*a2=c, a1+a2=-b, but what if a=/=1?

Thanks!

In one of my weekly posts, I have taken exactly this question: "How to factorize unusual quadratic equations?" The first example chosen is this one.
So you should check it out: http://www.veritasprep.com/blog/2013/12 ... equations/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Kudos [?]: 16942 [0], given: 230

Re: How to solve quadratics when a does NOT equal 1   [#permalink] 10 Sep 2014, 23:19
Similar topics Replies Last post
Similar
Topics:
31 Dec 1969, 17:00
3 Articles for solving quadratic equations using graphical approach 1 15 Sep 2016, 20:14
50 Solving Quadratic Inequalities: Graphic Approach 4 13 Aug 2017, 01:04
solving quadratic equations 3 09 Jun 2011, 02:34
5 How to solve quadratic equations - Factor quadratic equations 0 27 May 2017, 09:42
Display posts from previous: Sort by