Multiple choice

The number of real roots of the equation $\displaystyle \left ( x-1 \right )^{2}+\left ( x-2 \right )^{2}+\left ( x-3 \right )^{2}=0$ is

  1. $2$
  2. $1$
  3. $0$
  4. $3$
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C Correct answer
Explanation

For the sum of squares to be zero, each individual squared term must be zero. Since x-1=0, x-2=0, and x-3=0 cannot all be true simultaneously, there are no real roots.

AI explanation

Because the square of any real number must be greater than or equal to zero, the sum of the squares (x-1) squared, (x-2) squared, and (x-3) squared can only equal zero if each individual term is exactly zero. This would require x to equal 1, and x to equal 2, and x to equal 3 simultaneously, which is impossible for a single real number. Therefore, there are no real solutions to the equation.

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