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What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
 13 Feb 2013, 05:22
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What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ? (A) -8 (B) -4 (C) -2 (D) 4 (E) 8
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
13 Feb 2013, 05:28
carcass wrote: What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1|?
(A) -8
(B) -4
(C) -2
(D) 4
(E) 8 If |x - 1|>=0 ---->then the modulus will be equal to (x-1) & roots of the resulting equation will be 2,1 If |x - 1|<0 ---->then the modulus will be equal to (-x+1) & roots of the resulting equation will be 4,1 So the product of all the roots (2,1,4,1) is 8.
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
13 Feb 2013, 09:14
In order for |x - 1| to be equal to 1 - x, we would have to have x < 1 . Therefore eliminating your second pair of solutions You could also verify this by substituting x = 4 inthe original equation, and seeing that this solution DOES NOT fit. The only two solutions are 1 and 2. ANS: no correct option available Posted from my mobile device 
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
13 Feb 2013, 10:13
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
14 Feb 2013, 11:44
Bunuel wrote: carcass wrote: What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?
(A) -8
(B) -4
(C) -2
(D) 4
(E) 8 If x<1, then |x - 1| = -(x-1)=1-x, so in this case we'll have x^2 - 4x + 6 = 3-(1-x) --> x^2-5x+4=0 --> x=1 or x=4 --> discard both solutions since neither is in the range x<1. If x\geq{1}, then |x - 1| = x-1, so in this case we'll have x^2 - 4x + 6 = 3-(x-1) --> x^2-3x+2=0 --> x=1 or x=2. Therefore, the product of the roots is 1*2=2. No correct answer among the choices. Wow! Really? How often do we see this? Who the heck wrote this question?
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
15 Feb 2013, 03:43
vandygrad11 wrote: Bunuel wrote: carcass wrote: What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?
(A) -8
(B) -4
(C) -2
(D) 4
(E) 8 If x<1, then |x - 1| = -(x-1)=1-x, so in this case we'll have x^2 - 4x + 6 = 3-(1-x) --> x^2-5x+4=0 --> x=1 or x=4 --> discard both solutions since neither is in the range x<1. If x\geq{1}, then |x - 1| = x-1, so in this case we'll have x^2 - 4x + 6 = 3-(x-1) --> x^2-3x+2=0 --> x=1 or x=2. Therefore, the product of the roots is 1*2=2. No correct answer among the choices. Wow! Really? How often do we see this? Who the heck wrote this question? How often do we see what? I've seen similar question which reads: What is the product of all the solutions of x^2 + 4x + 7 = |x + 2| + 3 ?A. -6 B. -2 C. 2 D. 6 E. 12 OA: Try it. I'll provide solution for this question later, if necessary.
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
16 Feb 2013, 12:37
Bunuel wrote: How often do we see what? I've seen similar question which reads: What is the product of all the solutions of x^2 + 4x + 7 = |x + 2| + 3 ?A. -6 B. -2 C. 2 D. 6 E. 12 OA: Try it. I'll provide solution for this question later, if necessary. How often do we see no correct answer among the answer choices?
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 04:27
Bunuel wrote: carcass wrote: What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?
(A) -8
(B) -4
(C) -2
(D) 4
(E) 8 If x<1, then |x - 1| = -(x-1)=1-x, so in this case we'll have x^2 - 4x + 6 = 3-(1-x) --> x^2-5x+4=0 --> x=1 or x=4 --> discard both solutions since neither is in the range x<1. If x\geq{1}, then |x - 1| = x-1, so in this case we'll have x^2 - 4x + 6 = 3-(x-1) --> x^2-3x+2=0 --> x=1 or x=2. Therefore, the product of the roots is 1*2=2. No correct answer among the choices. I have a question, I do understand that why have you taken the value 1 but I don't understand why have you taken x>=1. Why not simply x>1
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 04:35
davidfrank wrote: Bunuel wrote: carcass wrote: What is the product of all the solutions of x^2 - 4x + 6 = 3 - |x - 1| ?
(A) -8
(B) -4
(C) -2
(D) 4
(E) 8 If x<1, then |x - 1| = -(x-1)=1-x, so in this case we'll have x^2 - 4x + 6 = 3-(1-x) --> x^2-5x+4=0 --> x=1 or x=4 --> discard both solutions since neither is in the range x<1. If x\geq{1}, then |x - 1| = x-1, so in this case we'll have x^2 - 4x + 6 = 3-(x-1) --> x^2-3x+2=0 --> x=1 or x=2. Therefore, the product of the roots is 1*2=2. No correct answer among the choices. I have a question, I do understand that why have you taken the value 1 but I don't understand why have you taken x>=1. Why not simply x>1 x could be 1, thus when you consider the ranges you should include this value in either of the range, so we could consider x<1 and x>=1 OR x<=1 and x>1 (you cam include = sign in either of the ranges). Hope it's clear.
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 04:48
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 06:16
I've seen similar question which reads: What is the product of all the solutions of x^2 + 4x + 7 = |x + 2| + 3 ?A. -6 B. -2 C. 2 D. 6 E. 12 OA: Try it. I'll provide solution for this question later, if necessary.[/quote] if |x+2|>=0 then |x+2|= (x+2) eqation becomes (x+2)(x+1)=0 x=-2,-1 if |x+2|<0 then |x+2|=-(x+2) equation becomes (x+2) (x+3) =0 x=-2,-3 ( can't be -2 since x<-2) product of the solution - -2*-1*-3= -6 Ans
Last edited by guerrero25 on 18 Feb 2013, 06:47, edited 1 time in total.
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 06:32
guerrero25 wrote: I've seen similar question which reads: What is the product of all the solutions of x^2 + 4x + 7 = |x + 2| + 3 ?A. -6 B. -2 C. 2 D. 6 E. 12 OA: Try it. I'll provide solution for this question later, if necessary. if |x+2|>=-2 then |x+2|= (x+2) eqation becomes (x+2)(x+1)=0 x=-2,-1 if |x+2|<-2 then |x+2|=-(x+2) equation becomes (x+2) (x+3) =0 x=-2,-3 ( can't be -2 since x<-2) product of the solution - -2*-1*-3= -6 Ans I guess you meant the following: When x\leq{-2}, then |x+2|=-(x-2). When x>{-2}, then |x+2|=(x-2). Complete solution: x^2 + 4x + 7 = |x + 2| + 3 --> x^2 + 4x + 4 = |x + 2| --> (x+2)^2=|x+2| --> (x+2)^4=(x+2)^2 --> (x+2)^2((x+2)^2-1)=0: x+2=0 --> x=-2; OR (x+2)^2-1=0 --> (x+2)^2=1 --> x=-1 or x=-3. The product of the roots: (-2)*(-1)*(-3)=-6. Answer: A. Hope it's clear.
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 06:48
Bunuel wrote: guerrero25 wrote: I've seen similar question which reads: What is the product of all the solutions of x^2 + 4x + 7 = |x + 2| + 3 ?A. -6 B. -2 C. 2 D. 6 E. 12 OA: Try it. I'll provide solution for this question later, if necessary. if |x+2|>=-2 then |x+2|= (x+2) eqation becomes (x+2)(x+1)=0 x=-2,-1 if |x+2|<-2 then |x+2|=-(x+2) equation becomes (x+2) (x+3) =0 x=-2,-3 ( can't be -2 since x<-2) product of the solution - -2*-1*-3= -6 Ans I guess you meant the following: When x\leq{-2}, then |x+2|=-(x-2). When x>{-2}, then |x+2|=(x-2). Complete solution: x^2 + 4x + 7 = |x + 2| + 3 --> x^2 + 4x + 4 = |x + 2| --> (x+2)^2=|x+2| --> (x+2)^4=(x+2)^2 --> (x+2)^2((x+2)^2-1)=0: x+2=0 --> x=-2; OR (x+2)^2-1=0 --> (x+2)^2=1 --> x=-1 or x=-3. The product of the roots: (-2)*(-1)*(-3)=-6. Answer: A. Hope it's clear. thanks ! That was a Typo . I edited the post .
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
18 Feb 2013, 06:52
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Re: What is the product of all the solutions of x^2 - 4x + 6=3 [#permalink]
25 Apr 2013, 07:23
Hello everyone,
I am so close to understanding this question, but the one thing I do not understand is why the positive of |x+2| is >= and the negative of |x+2| is just <?
Sorry if its a dumb question
Paul
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Re: What is the product of all the solutions of x^2 - 4x + 6=3
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25 Apr 2013, 07:23
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