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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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New post 19 Aug 2015, 02:36
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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

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

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New post Updated on: 09 Nov 2015, 08:15
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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.

Originally posted by ENGRTOMBA2018 on 19 Aug 2015, 04:42.
Last edited by ENGRTOMBA2018 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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New post 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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New post 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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Re: Find the product of the roots of the equation y [#permalink]

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New post 09 Nov 2015, 08:13
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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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Re: Find the product of the roots of the equation y [#permalink]

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New post 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
Please request an explanation :)
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Re: Find the product of the roots of the equation y [#permalink]

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New post 18 Aug 2017, 01:24
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Madhavi1990 wrote:
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
Please request an explanation :)



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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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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New post 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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New post 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]

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New post 23 Oct 2017, 13:28
Let z = |x|
then the equation becomes y = z^2 - 5z + 6
Solving for roots => z^2 - 5z + 6=0 => z = 2 or 3

so |x| = 2 => x = 2, -2
|x| = 3 => x = 3, -3

Multiplying (2, -2, 3, -3) = 36

Answer (D)
Re: Find the product of the roots of the equation y   [#permalink] 23 Oct 2017, 13:28
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