Quadratic Equations

[vinay1983]

lf 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

[Brent@GMATPrepNow]

lf 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: x^3 - x = (x - a)(x - b)(x - c)
Since the right side of the equation is factored nicely, let's factor the left side as well.

x^3 - x = x(x² - 1)
= (x)(x+1)(x-1)
Rearrange: = (x+1)(x)(x-1)

So, (x+1)(x)(x-1) = (x - a)(x - b)(x - c)
IMPORTANT: Notice that each part of the right side is in the form (x - something).
So, let's rewrite the left side in the same way

We get: (x - (-1))(x - 0)(x - 1) = (x - a)(x - b)(x - c)

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

So, b = 0

Answer: C

Cheers,
Brent