Find the roots of the polynomial x⁴ - 1. Give the multiplicity of each. A) Roots are x = 1, x = -1, x = i, x = -i, each with multiplicity 1. B) Roots are x = 1, x = -1, each with multiplicity 2. C) Root is x = 1 with multiplicity 4. D) Roots are x = 1, x = i, each with multiplicity 2. E) Roots are x = i, x = -i, each with multiplicity 2.

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Quizplus · Accepted Answer

The polynomial given is $x^4 - 1$, which can be factored into $(x^2 + 1)(x^2 - 1)$, further factoring $x^2 - 1$ into $(x + 1)(x - 1)$ and $x^2 + 1$ into $(x - i)(x + i)$, giving us the roots $x = 1, x = -1, x = i, x = -i$, each occurring only once, hence each with multiplicity 1.

Find the Roots of the Polynomial X4 - 1

Find the Roots of the Polynomial X⁴ - 1