Pre-Flashcard; 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 complex roots, counting multiplicities.

Front

How many zeros can a degree 4 polynomial have?

Back

A degree 4 polynomial can have 4 zeros, which can be real or complex.

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 a zero of a polynomial function?

Back

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

Front

If 2+3i is a zero of a polynomial function, what must another zero be?

Back

2-3i (the complex conjugate of 2+3i).

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

Can a polynomial have more zeros than its degree?

Back

No, a polynomial cannot have more zeros than its degree.

Front

What is a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_n*x^n + a_(n-1)*x^(n-1) + ... + a_1*x + a_0, where a_n, a_(n-1), ..., a_0 are constants.

Front

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

Back

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

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit.