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Retired Moderator V
Joined: 27 Oct 2017
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WE: Business Development (Energy and Utilities)
If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 84% (01:37) correct 16% (01:35) wrong based on 49 sessions

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If x is a number such that $$x^2-3x+2 = 0$$ and $$x^3+2x^2-x-2 = 0$$, what is the value of $$x+3$$?

A) 1
B) 2
C) 3
D) 4
E) 5

GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 1

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Retired Moderator V
Joined: 27 Oct 2017
Posts: 1320
Location: India
GPA: 3.64
WE: Business Development (Energy and Utilities)
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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Official Explanation:

$$x^2-3x+2 = (x-1)(x-2)$$

hence x = 1,2

No need to solve the cubic equation, $$x^3+2x^2-x-x=0$$, We can just substitute the value of x = 1, 2 in cubic equation to verify.

only x = 1 satisfy the equation, hence x =1

Question asks for value of x+3

hence Answer = x+3 = 4.
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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x^2−3x+2=0

i.e. (x+3) (x-1)
therefore x can be -3 or 1

x=1 satisfies the equation therefore x+3 = 4

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Joined: 08 Feb 2018
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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D.
Factorising the first quadratic gives x=2 and x=1, the second quadratic gives x=1,-2. For common value x=1, x+3 equals 4.
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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x^2-3x+2=0 and x^3+2x^2-x-2=0
A) 1
B) 2
C) 3
D) 4
E) 5

x^2-3x+2=0
which is x^2-2x-x+2=0
which is x(x-2)-1(x-2)=0
which means (x-1) (x-2)=0, which means 1 and 2 are roots of the equation

Now x^3+2x^2-x-2=0
which is x^2(x+2)-1(x+2)=0
which is (x^2-1)(x+2)=0
which is (x-1)(x+1)(x+2)=0. ..(as a^2-b^2 = (a-b)(a+b))
so x can be either 1, -1 or -2 i.e 1, -1 and -2 are roots of the cubic equation

Common root between the two equation(quadratic and cubic) is only 1 at which both equation becomes zero, hence x = 1
hence x+3= 4 is the answer

Originally posted by pk123 on 20 Oct 2018, 11:22.
Last edited by pk123 on 20 Oct 2018, 21:12, edited 2 times in total.
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Location: Viet Nam
Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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Below is my attempt

$$x^2$$ - 3x + 2 = 0 --> (x-2)(x-1) = 0 --> x =2 or x = 1
$$x^3$$ + 2$$x^2$$-x-2 = 0 --> (x+2)($$x^2$$-1) = 0 --> x = 1 or x = -1 or x = -2

Combine 2 solutions --> x = 1
--> x +3 = 4

Thank you!

Originally posted by yenbh on 20 Oct 2018, 11:23.
Last edited by yenbh on 20 Oct 2018, 20:49, edited 1 time in total.
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Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  [#permalink]

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This reply is hidden until the winner is announced. Re: If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0   [#permalink] 20 Oct 2018, 11:30
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# If x is a number such that x^2 - 3x + 2 = 0 and x^3 + 2x^2 - x - 2 = 0  