How many distinct roots does the polynomial P(x) = (x^2 + 1)^3 * (x - 2)^4 have in the complex field C?

Answer and explanation

Correct answer: C. 3 distinct roots (i, -i, and 2)

  1. Step 1: The roots are i (multiplicity 3), -i (multiplicity 3), and 2 (multiplicity 4). Step 2. The question asks for distinct roots: the distinct complex numbers are i, -i, and 2, which is 3 distinct roots. Answer: 3 distinct roots (i, -i, and 2). Why not the others: Total algebraic multiplicity is 3 + 3 + 4 = 10, but distinct values number 3.

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