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Chapter 2: Problem 1

The _____ _____ of _____ states that if \(f(x)\) is a polynomial of degree \(n(n>0),\) then \(f\) has at least one zero in the complex number system.

Short Answer

Expert verified
The Fundamental Theorem of Algebra fits in the blanks of the exercise statement.

Step by step solution

01

Identify the theorem

The statement in the exercise is referring to a foundational concept in algebra. The correct term that fits in the blanks is the 'Fundamental Theorem of Algebra'.
02

Understand the theorem

The Fundamental Theorem of Algebra states that every non-zero, single-variable, degree n polynomial with complex coefficients has, counted with multiplicity, exactly n roots. This essentially means that a degree n polynomial has exactly n roots in the complex number system.

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