College

Use the Fundamental Theorem of Algebra to find the number of complex roots of the polynomial, including any repeated roots.

\(-3x^3 - 2x - 13x^3 + 19x^2 + 12x + 14\)

Answer :

Final answer:

The given polynomial has 3 complex roots.


Explanation:

The given polynomial is:

-3x³ - 2x - 13x³ + 19x² + 12x + 14

Combine like terms to simplify the polynomial:

-16x³ + 19x² + 10x + 14

The Fundamental Theorem of Algebra states that a polynomial of degree n has exactly n complex roots. Since the degree of the given polynomial is 3, it has exactly 3 complex roots, including any repeated roots.


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