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The Fundamental Theorem of Algebra guarantees a polynomial of degree above 0 has at least what?
AOne rational zero
BTwo real zeros
CTwo turning points
DOne complex zero
Answer & Solution
Correct answer: D. One complex zero
1. Some polynomials have no real zeros at all, so a guarantee about real zeros would be false.
2. The Fundamental Theorem of Algebra promises at least one complex zero for any degree above 0.
3. Applying it repeatedly splits a degree n polynomial into n linear factors.
4. Rational zeros are not guaranteed, since the Rational Zero Theorem only supplies candidates to test.
_Source: OpenStax Precalculus (CC BY 4.0), section 3.6 Zeros of Polynomial Functions_
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