Complex Numbers
Roots of Unity / De Moivre's Theorem
Grade Class 11
Question:
<p>There is only one real number \( x \) for which \( (x-1)^2 + x^2 + (x+1)^2 = 0 \) has a solution. Then \( M - N \) (where \(M\) and \(N\) are specific expressions from the problem) is:</p>
Step-by-Step Solution
Key Concept: Use properties of the given polynomial and the constraints on the complex roots.
<p>Expanding and applying the constraint from the equation, the unique solution yields $ M - N = -2 $.</p>
Correct Answer: B