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# Find the product of the roots of the equation y

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Find the product of the roots of the equation y [#permalink]

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19 Aug 2015, 02:36
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Difficulty:

75% (hard)

Question Stats:

49% (01:01) correct 51% (01:07) wrong based on 376 sessions

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

(A) -36

(B) 6

(C) -6

(D) 36

(E) 0

Source : Aristotle Prep
[Reveal] Spoiler: OA

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Re: Find the product of the roots of the equation y [#permalink]

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19 Aug 2015, 04:42
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Gnpth wrote:
Find the product of the roots of the equation y = |x|2 - 5|x| + 6, where |x| is the modulus of x.

(A) -36

(B) 6

(C) -6

(D) 36

(E) 0

Source : Aristotle Prep

Gnpth, a small point, you can not find the roots of y = quadratic equation but can find the roots of quadratic equation = 0. Thus the question should be $$|x|^2-5|x|+6=0$$

Considering 2 cases,

Case 1, when x$$\geq$$0 --> |x| = x

Thus we get $$x^2-5x+6=0$$ ---> x = 2 or 3 and both of these are $$\geq$$0. Thus keep these.

Case 2, when x<0 --->|x| = -x

Thus we get $$x^2+5x+6=0$$ ---> x = -2 or -3 and both of these are $$<$$0. Thus keep these.

Therefore, the product of the roots = 2*3*-2*-3 = 36. D is the correct answer.
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Last edited by Engr2012 on 09 Nov 2015, 08:15, edited 2 times in total.
Corrected the typo

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Re: Find the product of the roots of the equation y [#permalink]

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09 Nov 2015, 06:42
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Engr2012,

This does not change the result, but i think you inverted the roots.

x^2−5x+6=0 ---> x = -2 or -3

x^2+5x+6=0 ---> x = +2 or +3

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Re: Find the product of the roots of the equation y [#permalink]

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09 Nov 2015, 07:14
Mascarfi wrote:
Engr2012,

This does not change the result, but i think you inverted the roots.

x^2−5x+6=0 ---> x = -2 or -3

x^2+5x+6=0 ---> x = +2 or +3

Thanks. Updated the solution.
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Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

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Re: Find the product of the roots of the equation y [#permalink]

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09 Nov 2015, 08:13
1
KUDOS
Expert's post
Engr2012 wrote:
Gnpth wrote:
Find the product of the roots of the equation y = |x|2 - 5|x| + 6, where |x| is the modulus of x.

(A) -36

(B) 6

(C) -6

(D) 36

(E) 0

Source : Aristotle Prep

Gnpth, a small point, you can not find the roots of y = quadratic equation but can find the roots of quadratic equation = 0. Thus the question should be $$|x|^2-5|x|+6=0$$

Considering 2 cases,

Case 1, when x$$\geq$$0 --> |x| = x

Thus we get $$x^2-5x+6=0$$ ---> x = -2 or -3 and both of these are $$\geq$$0. Thus keep these.

Case 2, when x<0 --->|x| = -x

Thus we get $$x^2+5x+6=0$$ ---> x = 2 or 3 and both of these are $$<$$0. Thus keep these.

Therefore, the product of the roots = 2*3*-2*-3 = 36. D is the correct answer.

hi,
the roots of $$x^2-5x+6=0$$ are 2 and 3 and not -2 and -3..
similarly for $$x^2+5x+6=0$$ roots are -2 and -3 and not 2 and 3..
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Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

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Re: Find the product of the roots of the equation y [#permalink]

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25 Nov 2015, 19:36
oh god, please have someone change the format of the question. I spent 2 minutes to understand that the question is not written correctly.

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Re: Find the product of the roots of the equation y [#permalink]

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02 Feb 2017, 20:41
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Re: Find the product of the roots of the equation y [#permalink]

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18 Aug 2017, 01:11
Engr2012 wrote:
Gnpth wrote:
Find the product of the roots of the equation y = |x|2 - 5|x| + 6, where |x| is the modulus of x.

(A) -36

(B) 6

(C) -6

(D) 36

(E) 0

Source : Aristotle Prep

Gnpth, a small point, you can not find the roots of y = quadratic equation but can find the roots of quadratic equation = 0. Thus the question should be $$|x|^2-5|x|+6=0$$

Considering 2 cases,

Case 1, when x$$\geq$$0 --> |x| = x

Thus we get $$x^2-5x+6=0$$ ---> x = 2 or 3 and both of these are $$\geq$$0. Thus keep these.

Case 2, when x<0 --->|x| = -x

Thus we get $$x^2+5x+6=0$$ ---> x = -2 or -3 and both of these are $$<$$0. Thus keep these.

Therefore, the product of the roots = 2*3*-2*-3 = 36. D is the correct answer.

have a query with one of the steps - when we do x<0 how come its still x square (positive) and not -x square?
I actually picked -36 cause -x^2 +5x +6 = 0 has roots as -3, 2

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Re: Find the product of the roots of the equation y [#permalink]

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18 Aug 2017, 01:24
1
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Expert's post
Engr2012 wrote:
Gnpth wrote:
Find the product of the roots of the equation y = |x|2 - 5|x| + 6, where |x| is the modulus of x.

(A) -36

(B) 6

(C) -6

(D) 36

(E) 0

Source : Aristotle Prep

Gnpth, a small point, you can not find the roots of y = quadratic equation but can find the roots of quadratic equation = 0. Thus the question should be $$|x|^2-5|x|+6=0$$

Considering 2 cases,

Case 1, when x$$\geq$$0 --> |x| = x

Thus we get $$x^2-5x+6=0$$ ---> x = 2 or 3 and both of these are $$\geq$$0. Thus keep these.

Case 2, when x<0 --->|x| = -x

Thus we get $$x^2+5x+6=0$$ ---> x = -2 or -3 and both of these are $$<$$0. Thus keep these.

Therefore, the product of the roots = 2*3*-2*-3 = 36. D is the correct answer.

have a query with one of the steps - when we do x<0 how come its still x square (positive) and not -x square?
I actually picked -36 cause -x^2 +5x +6 = 0 has roots as -3, 2

Hi..
A SQUARE will always be POSITIVE irrespective of the value of base..
So if x=-3.... $$x^2=(-3)^2=-3*-3=9$$

So a SQUARE of a non zero Number is always POSITIVE
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Re: Find the product of the roots of the equation y [#permalink]

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18 Aug 2017, 01:28
Thank you, was helpful. Got confused for a second because of the absolute value symbols

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Re: Find the product of the roots of the equation y [#permalink]

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18 Aug 2017, 02:52
For X>0
X^2-5X+6 roots 3,2
For X<0
X^2+5X +6 roots -3,-2

Product 36

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Re: Find the product of the roots of the equation y   [#permalink] 18 Aug 2017, 02:52
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