math 3 polynomial roots

Front

What is the degree of the polynomial f(x) = 5x^4 - 8x^3 + 4x^2 - 6x + 3?

Back

The degree is 4.

Front

How many roots can a polynomial of degree n have?

Back

A polynomial of degree n can have at most n roots.

Front

What is a root of a polynomial?

Back

A root of a polynomial is a value of x for which f(x) = 0.

Front

What does it mean if a polynomial has a root with odd multiplicity?

Back

It means the graph of the polynomial crosses the x-axis at that root.

Front

What does it mean if a polynomial has a root with even multiplicity?

Back

It means the graph of the polynomial touches the x-axis at that root but does not cross it.

Front

If a polynomial has complex roots, what can be said about their nature?

Back

Complex roots occur in conjugate pairs.

Front

What is the Fundamental Theorem of Algebra?

Back

It states that every non-constant polynomial has at least one complex root.

Front

How can you find the roots of a cubic polynomial?

Back

You can use factoring, synthetic division, or the cubic formula.

Front

What is synthetic division used for?

Back

Synthetic division is used to divide polynomials and find roots.

Front

What is the relationship between the coefficients of a polynomial and its roots?

Back

The sum and product of the roots can be related to the coefficients by Vieta's formulas.