What is the product of the roots of x^2 – 7|x| - 30 = 0?

Question

What is the product of the roots of  x^2 – 7|x| - 30 = 0 ?

A. -100
B. -9
C. 0
D. 9
E. 100

GMATinsight · Accepted Answer

x^2 – 7|x| - 30 = 0

i.e.  lxl^2 – 7|x| - 30 = 0

i.e.  lxl^2 – 10|x| + 3|x| - 30 = 0

i.e.   (lxl – 10)*(|x| + 3) = 0

i.e lxl = 10 or -3

But lxl can NOT be negative hence it can NOT be -3

i.e. lxl = 10

i.e. x = +10 or -10

Product of the roots = (+10)*(-10) = -100

ANswer: Option A

Lipun · Answer

x^2-7|x|-30  ----eqn(1). We need to check for two values of |x|.

When x>0, solving eqn(1) we get x=10
When x<0, the value of x will be negation of what we obtained for x>0. Thus, we get x=-10.

Product of roots: -100.

NitishJain · Answer

x^2–7|x|−30=0

Case 1: x> 0

x^2 -7x -30=0. => x^2 -10x +3x -30 =0
=> x = 10, -3; Since x >0, -3 is not possible

Case 2: x <0
x^2 +7x -30=0. => x^2 +10x -3x -30 =0
=> x = -10, 3; Since x<0 , 3 is not possible

Two roots: 10, -10

Product: -100

A

Doer01 · Answer

Hi  Bunuel , 
Why cannot this equation be solved by definition? Product of roots = c/a for any quadratic equation ax^2+bx+c=0 ?

AnkithaSrinivas · Answer

cause there is modulus involved

BrushMyQuant · Answer

We need to find what is the product of the roots of  x^2 – 7|x| - 30 = 0 ?

As we have |x| in the equation so we will have two cases 
 
   -   Case 1:  x ≥ 0 
=> |x| = x
=>  x^2 - 7x - 30 = 0 
=>  x^2 -10x + 3x − 30 = 0 
=> x*( x-10) + 3*(x - 10) = 0
=> (x - 10) * (x + 3) = 0
=> x = 10 or -3

But condition was x ≥ 0 
=>  x = 10 is a  SOLUTION   
  -   Case 2:  x ≤ 0 
=> |x| = -x
=>  x^2 + 7x - 30 = 0 
=>  x^2 + 10x - 3x − 30 = 0 
=> x*( x+10) - 3*(x + 10) = 0
=> (x + 10) * (x - 3) = 0
=> x = -10 or 3

But condition was x ≤ 0  
=>  x = -10 is a  SOLUTION

=> Product of the roots = 10 * -10 = -100

So,  Answer will be A 
Hope it helps!

Watch the following video to MASTER Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the product of the roots of x^2 – 7|x| - 30 = 0?

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

As we have \|x\| in the equation so we will have two cases
-Case 1: x ≥ 0 => \|x\| = x => \(x^2 - 7x - 30 = 0\) => \(x^2 -10x + 3x − 30 = 0\) => x( x-10) + 3(x - 10) = 0 => (x - 10) * (x + 3) = 0 => x = 10 or -3 But condition was x ≥ 0 => x = 10 is a SOLUTION	-Case 2: x ≤ 0 => \|x\| = -x => \(x^2 + 7x - 30 = 0\) => \(x^2 + 10x - 3x − 30 = 0\) => x( x+10) - 3(x + 10) = 0 => (x + 10) * (x - 3) = 0 => x = -10 or 3 But condition was x ≤ 0 => x = -10 is a SOLUTION

GMAT Problem Solving (PS) Questions

What is the product of the roots of x^2 – 7|x| - 30 = 0?

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards