What are the roots of the polynomial P(x) = x² (x² + 2x + 2)³, and what are their multiplicities? A) x = 0 with multiplicity 2, x = -1 + i with multiplicity 3, and x = -1 - i with multiplicity 3 B) x = 0 with multiplicity 2 C) x = 0 with multiplicity 2, x = -1 + i with multiplicity 1, and x = -1 - i with multiplicity 1 D) x = -1 + i with multiplicity 3, and x = -1 - i with multiplicity 3 E) x = 0 with multiplicity 2, x = -1 + i with multiplicity 2, and x = -1 - i with multiplicity 2

Question

Quizplus · Accepted Answer

The polynomial can be simplified to $x^2(x^2 + 2x + 2)^3$, indicating roots at $x = 0$ with multiplicity 2, and the quadratic $x^2 + 2x + 2$ has complex roots $x = -1 + i$ and $x = -1 - i$, each with multiplicity 3, due to the cubic exponent.

What Are the Roots of the Polynomial P(x) = X2

What Are the Roots of the Polynomial P(x) = X²