Last visit was: 23 Jul 2024, 11:12 It is currently 23 Jul 2024, 11:12
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# What is the product of the roots of the equation y = |x|^2 - 5|x| + 6

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94592
Own Kudos [?]: 643318 [27]
Given Kudos: 86728
Director
Joined: 09 Aug 2017
Posts: 686
Own Kudos [?]: 426 [2]
Given Kudos: 778
Intern
Joined: 11 Apr 2020
Posts: 4
Own Kudos [?]: 1 [1]
Given Kudos: 11
Location: India
Intern
Joined: 24 Aug 2020
Posts: 14
Own Kudos [?]: 6 [2]
Given Kudos: 31
Location: India
Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
2
Kudos
When the equation is in the form of $$y=ax^2+bx+c$$, the product of the roots of the equation is $$\frac{c}{a}$$.

The equation in the question can be split into two different equations $$x^2-5x+6$$ and $$x^2+5x+6$$ when $$x>6$$ and $$x<6$$ respectively.

The final answer is the product of the products of roots of these two equations. In each equation, the product is $$6/1=6$$. Hence the final answer is 36.
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6047
Own Kudos [?]: 4767 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
Bunuel wrote:
What is the product of the roots of the equation $$y = |x|^2 - 5|x| + 6$$?

(A) -36
(B) 6
(C) -6
(D) 36
(E) 0

Are You Up For the Challenge: 700 Level Questions

Find the product of the roots of the equation $$y = |x|^2 - 5|x| + 6$$, where |x| is the modulus of x.

Treat $$y = |x|^2 - 5|x| + 6$$ as $$y = x^2 - 5x + 6$$

Or, $$y = x^2 -3x - 2x + 6$$

Or, $$y = x(x -3) - 2( x - 3)$$

Or, $$y = (x -3)(x - 2)$$

Now if $$y = 0$$ we have $$x = 3 , 2$$

Now, initially we have assumed only the +ve values of $$y$$, as $$3 , 2$$, so the other possible values are $$-3 , -2$$

Thus, the product will be $$3*2*-3*-2 = 36$$, Hence Answer must be (D)
Non-Human User
Joined: 09 Sep 2013
Posts: 34045
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Re: What is the product of the roots of the equation y = |x|^2 - 5|x| + 6 [#permalink]
Moderator:
Math Expert
94592 posts