# 4.4 Theorems about Zeros of Polynomial Functions

Find a polynomial with specified zeros.

For a polynomial function with integer coefficients, find the rational zeros and the other zeros, if possible.

Use Descartes’ rule of signs to find information about the number of real zeros of a polynomial function with real coefficients.

We will now allow the coefficients of a polynomial to be complex numbers. In certain cases, we will restrict the coefficients to be real numbers, rational numbers, or integers, as shown in the following examples.

Polynomial | Type of Coefficient |
---|---|

$5{x}^{3}-3{x}^{2}+(2+4i)x+i$ | Complex |

$5{x}^{3}-3{x}^{2}+\sqrt{2}x-\pi $ | Real |

$5{x}^{3}-3{x}^{2}+\frac{2}{3}x-\frac{7}{4}$ | Rational |

$5{x}^{3}-3{x}^{2}+8x-11$ | Integer |

# The Fundamental Theorem of Algebra

A linear, or first-degree, ...

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