Fundamental Theorem of Algebra (Edited)

Front

What does the Fundamental Theorem of Algebra state?

Back

Every non-constant polynomial function has at least one complex root.

Front

How many roots does a polynomial of degree n have?

Back

A polynomial of degree n has exactly n roots, counting multiplicities.

Front

What is the degree of a polynomial?

Back

The degree of a polynomial is the highest power of the variable in the polynomial.

Front

If a polynomial has real coefficients, what can be said about its complex roots?

Back

Complex roots must occur in conjugate pairs.

Front

What is the relationship between the degree of a polynomial and the number of its zeros?

Back

The degree of a polynomial determines the maximum number of zeros it can have.

Front

What is a zero of a polynomial?

Back

A zero of a polynomial is a value of x that makes the polynomial equal to zero.

Front

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

Back

You can determine the number of real roots by analyzing the polynomial's degree and its graph.

Front

What is the significance of imaginary roots in polynomials?

Back

Imaginary roots indicate that the polynomial does not intersect the x-axis at those points.

Front

What is the degree of the polynomial f(x) = x^5 - 3x^3 + x?

Back

The degree of the polynomial is 5.

Front

How do you find the roots of a polynomial function?

Back

You can find the roots by factoring the polynomial, using the quadratic formula, or applying numerical methods.