Finding Zeros of Polynomials Flashcard

Front

What is the Conjugate Root Theorem?

Back

If a polynomial has a complex zero (a + bi), then its conjugate (a - bi) is also a zero.

Front

Given a complex zero 7-5i, what is the other zero according to the Conjugate Root Theorem?

Back

7+5i

Front

What does the Rational Root Theorem state?

Back

It provides a way to find all possible rational roots of a polynomial based on the factors of the constant term and the leading coefficient.

Front

What is the Fundamental Theorem of Algebra?

Back

It states that a polynomial of degree n has exactly n roots in the complex number system.

Front

Given a complex zero -12-8i, what is the other zero according to the Conjugate Root Theorem?

Back

-12+8i

Front

What is a polynomial?

Back

A mathematical expression consisting of variables, coefficients, and non-negative integer exponents.

Front

How do you find the zeros of a polynomial?

Back

By factoring the polynomial, using the quadratic formula, or applying synthetic division.

Front

What is a rational root?

Back

A root of a polynomial that can be expressed as a fraction of two integers.

Front

What is the degree of a polynomial?

Back

The highest power of the variable in the polynomial.

Front

What is synthetic division?

Back

A simplified method of dividing a polynomial by a linear binomial.