Multiple choice

The number of real roots of the equation $(x - 1)^2 + (x - 2)^2 + (x- 3)^2 = 0$ is :

  1. $1$
  2. $2$
  3. $3$

  4. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The sum of squares of real numbers is zero if and only if each term is zero. (x-1)^2 = 0, (x-2)^2 = 0, (x-3)^2 = 0. This requires x=1, x=2, and x=3 simultaneously, which is impossible. Therefore, there are no real roots.

AI explanation

The left hand side of the equation consists of perfect squares, meaning (x - 1)^2, (x - 2)^2, and (x - 3)^2 must all individually equal zero for their sum to be zero. This requires x to equal 1, 2, and 3 simultaneously, which is impossible for any real number. Therefore, there are zero real roots for this equation, meaning the correct response is None of these.

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