Fundamental Theorem of Algebra

Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial equation of degree n has exactly n roots in the complex number system, counting multiplicities.

Front

How do you find the zeros of a polynomial?

Back

To find the zeros of a polynomial, set the polynomial equal to zero and solve for the variable.

Front

What are the zeros of the polynomial f(x) = x^2 + 9x + 14?

Back

The zeros are -2 and -7.

Front

If a polynomial has 4 real roots and 2 complex roots, what is its degree?

Back

The degree of the polynomial is 6.

Front

What is the least degree of a polynomial that can have 5 as its highest root count?

Back

The least degree of the polynomial is 5.

Front

What is the remainder when dividing a polynomial by a linear factor?

Back

The remainder can be found using polynomial long division or synthetic division.

Front

What is synthetic division?

Back

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

Front

What is the relationship between the degree of a polynomial and the number of roots it can have?

Back

The degree of a polynomial indicates the maximum number of roots it can have, including real and complex roots.

Front

What is a complex root?

Back

A complex root is a solution to a polynomial equation that is not a real number, often expressed in the form a + bi, where i is the imaginary unit.

Front

How do you determine the number of real roots of a polynomial?

Back

The number of real roots can be determined using the discriminant of the polynomial or by analyzing its graph.