BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Q? Factoring quadratic eqn.

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Legendary Member
Posts: 502
Joined: Tue Jun 03, 2008 11:36 pm
Thanked: 99 times
Followed by:21 members

Q? Factoring quadratic eqn.

by vk_vinayak » Mon Aug 27, 2012 4:01 am
When solving a quadratic equation: x2 + 2x - 8 = 0

We know that sum -2 and + 4 equal to middle part and their product is equal to -8. We can safely write the factors as (x + a)(x + b) =0 ie (x-2)(x+4)=0

But, if the equation is 3x^2 + 5x -12 =0 , we come to know that a and b as +9 and -4. But we can't write it directly (x + 9)(x -4)=0 because of the quotient 3. We then need to divide 9 and -4 by 3. SO, we get the equation: (x+3)(x-4/3)=0.

Just wanted to confirm if this is a general rule (to divide the roots by co-ef of x^2) and works all the time.
- VK

I will (Learn. Recognize. Apply)
Top
Source: — Problem Solving |
User avatar
MBA Admissions Consultant
Posts: 2279
Joined: Fri Nov 11, 2011 7:51 am
Location: New York
Thanked: 660 times
Followed by:266 members
GMAT Score:770

by Jim@StratusPrep » Mon Aug 27, 2012 7:42 am
Your middle term will not work with this. Here is a good way to approach:

5x^2 + 11x + 2

Step 1: List the factors of the product of the coefficient and the last term 5(2) = 10 -- Factors are 1, 2, 5, and 10.
Step 2: Find the 2 factors that add up to the coefficient of the middle term 10 + 1 = 11
Step 3: Rewrite the middle term, splitting it with the factors your found in step 2 5x^2 + 10x + x + 2
Step 4: Factor grouped terms
5x(x+2)+1(x+2)= (5x+1)(x+2)
GMAT Answers provides a world class adaptive learning platform.
-- Push button course navigation to simplify planning
-- Daily assignments to fit your exam timeline
-- Organized review that is tailored based on your abiility
-- 1,000s of unique GMAT questions
-- 100s of handwritten 'digital flip books' for OG questions
-- 100% Free Trial and less than $20 per month after.
-- Free GMAT Quantitative Review

Image
Top
User avatar
Legendary Member
Posts: 502
Joined: Tue Jun 03, 2008 11:36 pm
Thanked: 99 times
Followed by:21 members

by vk_vinayak » Mon Aug 27, 2012 8:33 am
Jim@StratusPrep wrote:Your middle term will not work with this. Here is a good way to approach:

5x^2 + 11x + 2

Step 1: List the factors of the product of the coefficient and the last term 5(2) = 10 -- Factors are 1, 2, 5, and 10.
Step 2: Find the 2 factors that add up to the coefficient of the middle term 10 + 1 = 11
Step 3: Rewrite the middle term, splitting it with the factors your found in step 2 5x^2 + 10x + x + 2
Step 4: Factor grouped terms
5x(x+2)+1(x+2)= (5x+1)(x+2)
Jim, Thanks. I know the calculations, but I am looking for a shortcut.

After you figure out the factors as 10 and 1 (your step 2), I want to directly (without going through step 3 and 4) write the equation in the form of (x+a)(x+b)=0. It works perfectly when co-ef of x^2 is 1, but I was having problem when co-ef of x^2 as something else (eg: In your equation co-ef of x^2 is 5)

Here a=+10 and b=+1, but as the co-ef of x^2 is 5, I divided these a and b by 5, getting 2 and 1/5, so that I could write (x+2)(x+ 1/5)=0. I wanted confirm this method.
- VK

I will (Learn. Recognize. Apply)
Top
Post new topic Post Reply
• Page 1 of 1