Algebra
Textbooks
Boundless Algebra
Polynomials and Rational Functions
Algebra Textbooks Boundless Algebra Polynomials and Rational Functions
Algebra Textbooks Boundless Algebra
Algebra Textbooks
Algebra

Section 4

Zeroes of Polynomial Functions

Book Version 13
By Boundless
Boundless Algebra
Algebra
by Boundless
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5 concepts
The Fundamental Theorem of Algebra

The fundamental theorem states that every non-constant single-variable polynomial with complex coefficients has at least one complex root.

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Finding Polynomials with Given Zeros

To construct a polynomial from given zeros, set $x$ equal to each zero, move everything to one side, then multiply each resulting equation.

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Finding Zeros of Factored Polynomials

The factored form of a polynomial reveals its zeros, which are defined as points where the function touches the $x$-axis.

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Integer Coefficients and the Rational Zeros Theorem

Each solution to a polynomial, expressed as $x= \frac {p}{q}$, must satisfy that $p$ and $q$ are integer factors of $a_0$ and $a_n$, respectively.

The Rule of Signs

The rule of signs gives an upper bound number of positive or negative roots of a polynomial.

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