Fundamental Theorem of Algebra

Front

What does the Fundamental Theorem of Algebra state?

Back

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

Front

How many roots does a polynomial of degree 4 have?

Back

4 roots.

Front

What is a polynomial function?

Back

A mathematical expression involving a sum of powers in one or more variables multiplied by coefficients.

Front

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

Back

The degree is 4.

Front

If a polynomial has a degree of 5, how many solutions can it have?

Back

It can have 5 solutions.

Front

What are complex roots?

Back

Roots that include imaginary numbers, typically in the form a + bi, where a and b are real numbers.

Front

What is the significance of multiplicity in polynomial roots?

Back

Multiplicity refers to the number of times a particular root is repeated in a polynomial.

Front

How do you find the roots of a polynomial?

Back

By factoring the polynomial, using synthetic division, or applying the quadratic formula for degree 2 polynomials.

Front

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

Back

The coefficients of a polynomial can be expressed in terms of its roots using Vieta's formulas.

Front

What is a zero of a polynomial function?

Back

A value of x for which the polynomial evaluates to zero.