Multiple choice

The product of the roots of the equation $(x - 2)^2 - 3(x - 2) + 2 = 0$ is

  1. $-12$
  2. $12$
  3. $7$
  4. $-7$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let y = x - 2. The equation becomes y^2 - 3y + 2 = 0. Factoring gives (y - 1)(y - 2) = 0, so y = 1 or y = 2. Substituting back, x - 2 = 1 (x = 3) or x - 2 = 2 (x = 4). The product of roots 3 * 4 is 12.

AI explanation

Treating the given expression as a quadratic in terms of (x minus 2), we factor it to get ((x minus 2) minus 1)((x minus 2) minus 2) equals 0. This simplifies to (x minus 3)(x minus 4) equals 0, yielding roots of 3 and 4. The product of these roots is 3 times 4, which equals 12.

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