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If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)

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Joined: 11 Sep 2015
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GMAT 1: 770 Q49 V46
Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)  [#permalink]

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New post 24 Jul 2018, 05:12
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Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3



Given: x³ - x = (x - a)(x - b)(x - c)
Factor x from left side: x(x² - 1) = (x - a)(x - b)(x - c)
x² - 1 is a difference of squares, so we can factor that: x(x + 1)(x - 1) = (x - a)(x - b)(x - c)
Rewrite first 2 terms as: (x - 0)(x - -1)(x - 1) = (x - a)(x - b)(x - c)
Rearrange as: (x - 1)(x - 0)(x - -1) = (x - a)(x - b)(x - c)

Since, we're told that c < b < a, we can see that a = 1, b = 0 and c = -1

Answer: C

Cheers,
Brent
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Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)  [#permalink]

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Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)   [#permalink] 01 Aug 2019, 02:10

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