If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu

Question

If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the value of |m - n| ?

A. 0
B. 1
C. 2
D. 9
E. 18

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firas92 · Accepted Answer

x^2 - 7|x| - 18 = 0

x=0  is obviously not a solution so  x  is either positive or negative

Case 1: When  x  is positive ( |x|=x )  ,

x^2 - 7|x| - 18 = 0  becomes  x^2 - 7x - 18 = 0

Or  (x-9)(x+2)=0  so  x=9  or  -2

But since in this case  x  is positive,  x=9  is only possible root

m=9

Case 2: When  x  is negative ( |x|=-x )  ,

x^2 - 7|x| - 18 = 0  becomes  x^2 + 7x - 18 = 0

Or  (x+9)(x-2)=0 , so  x=-9  or  2

But since in this case  x  is negative,  x=-9  is only possible root

n=-9

Therefore  |m-n| = |9-(-9)| = 18

Answer is  (E)

GMATinsight · Answer

i.e. x^2 - 7|x| - 18 = 0

i.e. lxl^2 - 7|x| - 18 = 0

i.e. |x|(|x|-9)+2(|x|-9)=0

i.e. (|x|-9)(|x|+2)=0

i.e. |x|=9 or -2

But lxl is never negative hence lxl = 9

i.e. x = -9 and +9 which are the values of m and n hence

lm-nl = l-9-9l = 18

Answer: Option E

yashikaaggarwal · Answer

Sir, shouldn't roots be -9,&2 or -2&9
Because (x+9)(x-9) quadratic equation is x^2-81
Kindly Revert

Posted from my mobile device

abannore · Answer

x^2 -7|x|-18=0
 |x|^2 -7|x|-18=0 --> ( x^2  can be written as  |x|^2 )
 |x|^2 -9|x|+2|x|-18=0 
|x|(|x|-9)+2(|x|-9)=0
(|x|-9)(|x|+2)=0
|x|=9 or -2

Since modulus value is never negative, discard |x|=-2
Solution of equation: 
|x|=9
x=9 or x=-9

Sum of solutions of the above equation = |9-(-9)|=18

Answer: E

GMATinsight · Answer

yashikaaggarwal

-2&9 are the values of lxl and not of x

but lxl can not be -ve so -2 is out anyway 2 and -2 do NOT satisfy the equation

so we are left with

lxl = 9

ie.. x = +9 or -9

I hope that help

sambitspm · Answer

See the attachment.
E - 18

BrushMyQuant · Answer

m and n are the roots of x^2 - 7|x| - 18 = 0 and we need to find the value of |m - n|

As we have \|x\| in the equation so we will have two cases
-Case 1: x ≥ 0 => \|x\| = x => \(x^2 - 7x - 18 = 0\) => \(x^2 − 9x + 2x − 18 = 0\) => x * ( x-9) + 2(x - 9) = 0 => (x - 9) (x + 2) = 0 => x = 9 or -2 But condition was x ≥ 0 => x = 9 is a SOLUTION	-Case 2: x < 0 => \|x\| = -x => \(x^2 + 7x - 18 = 0\) => \(x^2 + 9x - 2x − 18 = 0\) => x * ( x+9) - 2(x + 9) = 0 => (x + 9) (x - 2) = 0 => x = -9 or 2 But condition was x < 0 => x = -9 is a SOLUTION

=> Both one of m or n is 9 and other is -9
=> |m -n| = |9-(-9)| = |18| = 18 OR
|m -n| = |-9-9| = |-18| = 18 OR

So, Answer will be E
Hope it helps!

Watch the following video to MASTER Absolute Values

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If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu

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If m and n are the roots of x^2 - 7|x| - 18 = 0, then what is the valu

Prep Toolkit

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