Multiple choice

What is the number of real roots of the equation (x - 1)2 + (x - 3)2 + (x - 5)2 = 0?

  1. None

  2. Only one

  3. Only two

  4. Three
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A Correct answer
Explanation

A sum of squares equals zero if and only if each term is zero. (x-1)^2=0, (x-3)^2=0, (x-5)^2=0. This implies x=1, x=3, and x=5 simultaneously, which is impossible. Thus, there are no real roots.

AI explanation

The equation consists of three squared terms summing to zero. Because the square of any real number cannot be negative, the only way for their sum to be zero is if each term is individually equal to zero. Setting the terms to zero requires x to equal 1, 3, and 5 simultaneously, which is impossible for a single real number. Therefore, the equation has no real roots.

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