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# If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what

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Math Expert
Joined: 02 Sep 2009
Posts: 59590
If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what  [#permalink]

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07 Apr 2019, 21:22
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Difficulty:

5% (low)

Question Stats:

88% (01:11) correct 12% (01:37) wrong based on 51 sessions

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If both expressions $$x^2 – 3x + 2$$ and $$x^2 – 4x + 3$$ equal 0, then what is the value of $$(x – 3)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

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Joined: 18 Aug 2017
Posts: 5447
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
Re: If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what  [#permalink]

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08 Apr 2019, 01:06
1
Bunuel wrote:
If both expressions $$x^2 – 3x + 2$$ and $$x^2 – 4x + 3$$ equal 0, then what is the value of $$(x – 3)^2$$ ?

(A) 0
(B) 1
(C) 2
(D) 3
(E) 4

$$x^2 – 3x + 2$$ and $$x^2 – 4x + 3$$ equal 0
(x-2)(x-1) and (x-3)(x-1)
x-1 is common so x= 1
$$(x – 3)^2$$
= > 4
IMO E
Senior Manager
Joined: 12 Sep 2017
Posts: 308
If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what  [#permalink]

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09 Apr 2019, 18:29
Just equal both equations:

$$x^2 – 3x + 2 = x^2 – 4x + 3 = 0$$

$$– 3x + 4x = 3 - 2$$

$$x = 1$$

$$(x - 3)^2$$

$$(1 - 3)^2$$

$$(-2)^2$$

$$4$$

E
Intern
Joined: 04 Jul 2019
Posts: 4
Re: If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what  [#permalink]

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10 Aug 2019, 09:14
1
Since both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0
=> (x-1)(x-2) = 0 and (x-1)(x-3) =0 , (x-1) is the common factor in both expressions which makes these expressions 0
therefore, (x-1) must be 0
=> x=1

=> (x-3)^2 = 4, Ans E.
Re: If both expressions x^2 – 3x + 2 and x^2 – 4x + 3 equal 0, then what   [#permalink] 10 Aug 2019, 09:14
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