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Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.______
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Q. Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.______
- Fundamental Theorem of Algebra: The Fundamental Theorem of Algebra states that every non-zero, single-variable, degree polynomial with complex coefficients has, counted with multiplicity, exactly roots in the complex number system. To apply this theorem, we first need to determine the degree of the given polynomial.The given polynomial is . The highest power of in the polynomial is , which means the degree of the polynomial is .
- Determining the Degree: According to the Fundamental Theorem of Algebra, a polynomial of degree will have exactly roots in the complex number system. Since we have established that the degree of our polynomial is , it follows that there will be exactly complex roots for the polynomial . These roots could be real or non-real complex numbers, and some of them could be repeated.
