Multiple choice

The number of real root of the equation ${(x - 1)^2} + {(x - 2)^2} + {(x - 3)^2} + {(x - 4)^2} + ..... + {(x - n)^2} = 0$

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

A sum of squares of real numbers is zero if and only if each individual term is zero. This would require x=1, x=2, ..., x=n simultaneously, which is impossible for n > 1. Thus, there are no real roots.

AI explanation

The sum of squares of real numbers is zero only if each individual square is zero. For the sum of (x-1)^2 + (x-2)^2 + ... + (x-n)^2 to equal zero, x would need to equal 1, 2, and n simultaneously. Because this is impossible for any single real value of x, the equation has no real roots. The number of real roots is 0.

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