Complex Zeros Practice

Front

What is a complex zero?

Back

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

Front

What is the Conjugate Root Theorem?

Back

The Conjugate Root Theorem states that if a polynomial has real coefficients and a complex zero a + bi, then its conjugate a - bi is also a zero of the polynomial.

Front

How do you determine the number of real zeros in a polynomial?

Back

The number of real zeros can be determined using the Fundamental Theorem of Algebra, which states that a polynomial of degree n has exactly n zeros (real or complex), and by analyzing the polynomial's graph.

Front

What is the Fundamental Theorem of Algebra?

Back

The Fundamental Theorem of Algebra states that every non-constant polynomial equation of degree n has exactly n complex roots, counting multiplicities.

Front

How do you find the zeros of a polynomial function?

Back

To find the zeros of a polynomial function, set the polynomial equal to zero and solve for the variable using factoring, synthetic division, or the quadratic formula.

Front

What is a polynomial function of least degree?

Back

A polynomial function of least degree is the simplest polynomial that has the given zeros, meaning it has the lowest possible degree while still containing all specified roots.

Front

What are rational zeros?

Back

Rational zeros are solutions to a polynomial equation that can be expressed as a fraction p/q, where p is a factor of the constant term and q is a factor of the leading coefficient.

Front

How do you apply the Rational Root Theorem?

Back

The Rational Root Theorem helps identify possible rational zeros of a polynomial by listing all possible fractions formed by the factors of the constant term and the leading coefficient.

Front

What is the significance of the degree of a polynomial?

Back

The degree of a polynomial indicates the highest power of the variable, which determines the number of zeros and the behavior of the polynomial's graph.

Front

How can you verify if a number is a zero of a polynomial?

Back

To verify if a number is a zero of a polynomial, substitute the number into the polynomial equation. If the result is zero, then it is a zero.